Talk:Quantum state/Archive 1

3713:

I would say that by 'phenomenon', Bohr means 'process observed and described'. He is not referring to what I would think of as Einstein's idea of a natural process that happens whether or not someone later observes it. Obviously, an account or description of an unobserved process is to a large extent a theoretical speculation. Quantum mechanics is a method of description of experiments. Bohr thinks it ineluctably involves preparation and detection as ingredients of phenomena. The preparation is specified by a generation of an initial 'state' and the detection determines the specification of a final 'state'. Sometimes they are the same. The quantum 'states' are specified in terms of appropriate 'configuration' spaces. Unlike classical mechanics using states in phase space, quantum mechanics using 'configuration' space 'states' cannot in general support deterministic predictions, although the Schrödinger equation itself is deterministic as noted by von Neumann, and a 'phenomenon' is a determinate actual physical entity.

3066:

clearly wrong. It could mean, however, that it is possible to represent all possible values of the observable exactly in a mathematical sense, (e.g. as an exact solution to a PDE such as Schrodinger's equation). This second sense is, in principle, correct. However, the nuance should be made clear, and it should also be mentioned that in practice, such an "exact" solution is achievable via certain routes (e.g. Hartree-Fock) but often not feasible due to computational workload, especially for large systems. In this case, methods such as density functional theory are used, wherein the "mathematically exact" sense of the ambiguous statement also becomes false (DFT represents the electrostatic potential of a quantum system exactly but only approximates exchange/correlation interactions).

269:

the amplitude means. Its norm is the probability of finding the parameter in the described state when a device for measuring that parameter is used to make a measurement. Often, the measurable parameter is simply a classically defined particle attribute, such as its position or spin, but it can also be defined at a more grossly sensible level as, e.g., a detection recognized by photon detector number 3. My experience is limited here, inasmuch as I am not even a physicist, let alone a quantum physicist, but I think a definition along these lines could be improved by an expert who would take into account problems posed by conjugate pairs of attributes and vectors that define both continuous attributes (e.g., position) and discrete attributes (e.g. spin).

4727:. A phase space description supplies twice as much information as a configuration space description. In classical mechanics, it is supposed that a phase space description is available. This supports a precise determination of the future of the system. With only half the information available in a configuration space description, it cannot support a precise determination of the future of the system; this is true for both classical and quantum mechanics. This was expressed by Heisenberg as follows: "But in the rigorous formulation of the law of causality — "If we know the present precisely, we can calculate the future" — it is not the conclusion that is faulty, but the premise. We simply cannot know the present in all its parameters."< 4002:"A state of a system may be defined as an undisturbed motion that is restricted by as many conditions or data as are theoretically possible without mutual Interference or contradiction. In practice, the conditions could be imposed by a suitable preparation of the system, consisting perhaps of passing it through various kinds of sorting apparatus, such as slits and polarimeters, the system being undisturbed after preparation. The word 'state' may be used to mean either the state at one particular time (after the preparation), or the state throughout the whole of the time after the preparation. To distinguish these two meanings, the latter will be called a 'state of motion' when there is liable to be ambiguity."< 3563:"The tautology in the opening sentence here is unfortunate, but mostly unavoidable. If any Wikipedian can come up with a precise, friendly definition of a quantum state, then I'd give them a hearty slap on the back, because the fact is that no such definition exists. Quantum mechanics is somewhat self-referential in that respect. A state is how something is. Two states are the same if there is no way to tell them apart via a measurement. That's about the sum of it. Between this and the fuzziness of the definition of 'measurement', you'll find that circular logic is just about unavoidable when dealing with the fundamentals of QM." 491:

called degenerate states." For example, there are four distinct n=2 states in hydrogen (one 2s, three 2p). In the absence of any external field, they are precisely degenerate. They form an energy level. However, they are quite clearly not the same quantum state, as they result in different values for other observables, such as the electron's angular momentum, or it's projection. Thus, and energy level can contain many quantum states and it is not appropriate to merge this topic with the quantum state topic. I propose we remove the suggestion to merge the energy level article with this one.

3753:

choice of momentum space or configuration space, or whatever) that we observe. That is the ineluctable limitation on knowledge of state to which Heisenberg is referring, imposed by the quantum mechanical kinematics. A quantum phenomenon becomes determinate only when it has been detected, as pointed out below by Rosenfeld. Its initial condition as specified by quantum kinematics does not determine it. This contrasts with the classical kinematics which allow a state description that supports exact determination of the future.

4310:

somewhere that it's the right thing to do. I don't want to spend time becoming a Wikilawyer, searching out the policy details. I have already posted above what seems to me to cover the matter, with no response to the point about propriety of behaviour. At the same time I don't want to knuckle under to people who disagree with your view that "generally one should give reasons when reverting". Yes, I can put up with undoing of my edits, but I expect some immediate reason on the talk page.

4346:

being entirely uncited, I really can't tell what particular points you are trying to convey. I understand that there may be an issue with language barriers, so perhaps you can explain here what you are trying to add to the article, and maybe we can work together to draft a better version? Thanks " and "I'm afraid I'm having a hard time following you here." Am I being asked to give the writer of that some tutorials in English? If so, I have to say 'Sorry, I don't offer that service'.

4694:. This is because if it is further passed through a copy of the analyser, it emerges entirely through the copy-same output channel. The mixed state cannot be described by a wave function, because it would emerge riven into many sub-beams, one for every output channel of the analyser. A copy of the system in the mixed beam has definite respective probabilities of emerging in the several output channels of the analyser. The mixed beam probabilities are expressed in a density matrix. 4058:

state. Even though it is not yet observed, it is still causally conditioned by the observer, not in a native state. For example, it might have been prepared in a definite state of uniform motion in a nearly straight line if it is observed in a place in space where there is nearly no gravity. Then it is in a momentum eigenstate. It has no definite position. Its momentum can be measured by its angle of deflection by a diffraction grating and detection by a suitably placed device.

2841:

typical textbook which follows this interpretation is "Modern Quantum Mechanics" by Sakurai (who even talks about such strange things as "pure ensembles"). Unfortunately, from the point of view of people who believe that the state can contain complete information about the system (and solve the "measurement problem" by other means, e.g., decoherence), this statement is very wrong. It is the measurement setups which "show statistical behavior", not states.

31: 3735:"But that a revision of kinematical and mechanical concepts is necessary seems to follow directly from the basic equations of quantum mechanics. .... But what is wrong in the sharp formulation of the law of causality, "When we know the present precisely, we can predict the future," is not the conclusion but the assumption. Even in principle we cannot know the present in all detail."< 4041:"... every atomic phenomenon is closed in the sense that its observation is based on registrations obtained by means of suitable amplification devices with irreversible functioning such as, for example, permanent marks on the photographic plate caused by the penetration of electrons into the emulsion ..."<Bohr (1958) quoted by Wheeler, Zurek (1983), page viii.: --> 4878:"All the same the mathematics is only a tool and one should learn to hold the physical ideas in one's mind without reference to the mathematical form. In this book I have tried to keep the physics to the forefront, by beginning with an entirely physical chapter and in the later work examining the physical meaning underlying the formalism wherever possible." 3579:

expresses the views of Niels Bohr, insists that physics must be reported on the primary foundation of ordinary language. The other leading principal exponent of the Copenhagen interpretation, Werner Heisenberg, accepts this. It is true that occasionally on this page some reference to the Copenhagen interpretation has been made in terms that ridicule it.

256:

self-referential in that respect. A state is how something is. Two states are the same if there is no way to tell them apart via a measurement. That's about the sum of it. Between this and the fuzziness of the definition of 'measurement', you'll find that circular logic is just about unavoidable when dealing with the fundamentals of QM.

557:, vibrational and rotational energy levels in molecules, and energy level transitions between electronic, vibrational, and rotational energy levels, and photon emission and absorption in a practical sort of way, as opposed to a rather theoretical physics discussion (well - matter of opinion). Upon briefly reviewing both articles, I think 2617:. It theorizes that quantum state tries to provide as much as possible the statistical properties of an ensemble of similarly prepared systems. However, sometimes, it can not give a complete description of the system. The other interpretation is exemplified by the Copenhagen interpretation and championed by eminent physicists 143:

been said, the reality of quantum mechanics is hotly debated and I don't think anyone has yet come up with a satisfactory answer. It's worth noting that 'quantum mechanics' in itself is not a complete theory; it works best when extended with Quantum Field Theory, which makes a little more sense though is even more complicated.

375:). Rather, this article should have a section on stationary states, with a {{main|stationary state}} tag linking to the big article about eigenstates of the hamiltonian (strictly speaking, I think an energy level is an eigenvalue, not an eigenstate, so it's not a quantum state, right? so the proper article to link to is 2606: 134:

of a quantum state. Since everything in the Universe is quantum, including the measuring devices, the idea that the result of a measurement is somehow more 'real' can only be a shorthand for the particular type of quantum state which is produced by interactions with a measuring device and the environment.

4510:

I have some appreciation for what you mean. If people always substitute the mathematics for physical reality, they will misunderstand enormous conceptual shifts such as the ones that took place in the development of thermodynamics from 1820 to 1890. Here people often wrestled with verbal formulations

4265:

I think what you're being asked to do now is to suggest (on this talk page) a specific change to the wording of the article. How would you write the opening paragraph, for example? Of course, you don't have to do it that way, you can just as well make changes to the article directly, provided you can

4057:

Nevertheless, Dirac's state is defined as exhaustively as is theoretically possible for a quantum system. This makes it a pure state. The pure state is not that of a raw natural object, such a an atom of silver vapour escaping through a small hole in an oven wall. No, it is an artificially prepared

4053:

A physical entity that is indeterminately defined can have future adventures only probabilistically. Being indeterminate, it cannot have a determined future. This contrasts with a determinate classical physical object, which can have a determined future. That is one difference between Dirac's quantum

3500:

I reverted the edit because I found it largely incomprehensible. In addition to the last three paragraphs being entirely uncited, I really can't tell what particular points you are trying to convey. I understand that there may be an issue with language barriers, so perhaps you can explain here what

3408:

Don't revert a large edit because much of it is bad and you don't have time to rewrite the whole thing. Instead, find even a little bit of the edit that is not objectionable and undo the rest. (To do this, you can use the "undo" button, then type back in what you want to keep). As long as you keep

2406:

A13ean, you are saying that the spin of the electron may be entangled with the spin of the proton. Well, that's true. But the position of the electron is also entangled with the position of the proton. (The proton is not infinitely heavy.) At a greater level of accuracy, both the position and spin of

2387:

I would strongly suggest keeping the discussion in the lead to the non-spin quantum numbers, and explicitly mention that spin is being neglected there. Most texts introduce quantum states this way, and even for hydrogen the spin states are more complicated than you would want to go into in the lead.

1899:

From what I have read, written by some of the greats in the field, I am not sure that there is a single understanding of what a "state" is. So I think you need not be too critical of your own writing. If we can get beyond the state of having something that "isn't even wrong," then we can hope to make

1845:

They appear to use confusing notation in the example, it seems they should have used P(0) and Q(0) for the initial state. They should have then explained that P(t) and Q(t) were functions for how these values change in time. In this particular case P(t) is the function for the momentum whilst Q(t) is

739:

The conceptual introduction is excellent. It provides an explanation of quantum states in relation to classical mechanics in a way that's very accessible to a layman (like myself). In fact, it's one of the best explanations of this type I've seen. And it's even structured properly: general aspects

490:

with quantum state. A quantum state is a distinct entitity, with a number of observables, only one of which is it's (eigen) energy. The energy level entry needs improvement, and should state something like the following: "Multiple states may have the same value of the energy, in which case they are

306:

IMHO that would be misplaced in this context, this page being a general description of states in quantum theory. Matter / antimatter states are a specific feature of quantum field theory (i.e. quantum theory + special relativity), and annihilation processes are in fact a question of scattering theory

4363:

I think my question is quite reasonable in the light of the literature about quantum mechanics. If I don't get a response here and now, I can hardly expect reasonable responses further on. My question is about the basic conceptual framework of the article. If that can't be discussed, then it is open

3752:

I have inserted the items to bring out the relevance of Heisenberg's remarks here to the notion of quantum state. Also the kinematics are the description of the 'state'. As Dirac points out below, what we can know is determined by our mode of construction of the artificial state (e.g. our necessary

3712:

Bohr's thought continued to develop long after the early days. He eventually settled on the idea of a 'phenomenon'. He refers to the just-quoted paper in his celebrated attack on Einstein in the 1949 Schilpp book. Here below, Rosenfeld and Wheeler note this culminating concept. In ordinary language,

3622:

enables us to follow the course of a physical process in so far as it is quantum-mechanically determinate; not in a causal sense, but in a statistical one. Every process consists of elementary processes which we are accustomed to call transitions or jumps; the jump itself seems to defy all attempts

3439:

The first and foremost alternative to reverting when you find you disagree with an edit is to find a third version of the text that incorporates at least some of the elements of the prior text and the current text. Sometimes that's as easy as making the article state that there is controversy about

3422:

Never revert an edit because it was made via an improper process. Reversion is not a proper tool for punishing an editor or retaliating or exacting vengeance. No edit, reversion or not, should be made for the purpose of teaching another editor a lesson or keeping an editor from enjoying the fruits

3394:

Even if you find an article was slightly better before an edit, in an area where opinions could differ, you should not revert that edit, especially if you are the author of the prior text. The reason for this is that authors and others with past involvement in an article have a natural prejudice in

3267:

is of the addition kind. The phrase 'major change' might be considered ambiguous. The just above talk page comment about the edit says it was not intended as a change to substantial underlying principles. I read that as meaning that the warnings about "caution" apply to "large proposed deletions or

268:

Mathematically, a quantum state is a unit vector in a complex Hilbert space. The question is: What do the elements of that vector represent? Each element has two parts (1) a description of a the state of a measurable parameter of the system and (2) an amplitude. There is little question about what

133:

Technical point: The description of the quantum state as formal and non-physical, as against 'real' measurements, is highly debatable. In many accounts of quantum measurement the quantum state (density matrix) is the _only_ physical reality, the results of a measurement also being expressed in terms

4169:

A mathematical entity can be directly, though incompletely, expressed in symbols and words, and can be exercised directly in mathematical propositions, but this is not true of a physical entity. A mathematical entity has a timeless and placeless existence, but this is not true of an actual physical

4161:

Ultimately, the distinction between a physical and mathematical entity requires an exercise of conceptual skills and intuition and cannot be reduced to a mere word game. One can show or exercise the difference, but one cannot completely put it into words. Nevertheless, for an encyclopaedia, such as

4016:

No mention here of mathematical objects. Dirac is referring to physical objects. He distinguishes between an instantaneous state and a state with an indeterminate duration in time. The state so defined is physically indeterminate because it it not actually observed by detection. That is the meaning

2421:

LaoChen, I think what you wrote is pretty good, except that it implies that all possible states are specified by the four quantum numbers. But in reality, it is quite possible for an electron to be in a superposition of 1s and 3p or whatever. :-) (I know that this problem was already in the article

725:

i think the section you added is fine, although it could be more succinct, and gives sufficient reason to remove the "context" template, the problem with the intro pointed out by Steve below notwithstanding. the neglected state of the "mathematical formulation" section can probably be blamed on me.

100:

What is the point of writing an article like this? What is the target audience? Possibly only the person(s) who wrote it and a few others. It needs to be carefully rewritten bearing in mind always how the reader might be struggling. I have a 1st degree in Maths and I am spending ages just trying to

5777:

In a word, no. Nobody who has a reasonable knowledge of quantum mechanics doubts that "measurement" usually disturbs the system. If you think you know of some exception to this, please say so. Interpretive questions are asked about the nature of the disturbance, but not about its universally usual

4681:

The first stage of the "preparation" is typically the production of a beam of independent copies of the system, for example a beam of metal atoms from a small hole in the wall of an oven containing metal vapour. If that raw beam is taken as the final product of the "preparation" at that stage, the

4213:

Last time I posted something here, it was undone without an immediate talk page explanation, but with an edit summary that said "let's discuss on talk page before adding". No acknowledgement was forthcoming that such an undo, lacking an immediate talk page comment, was a breach of proper editorial

3350:

Another kind of acceptable reversion is an incidental one. A Knowledge editor is not expected to investigate the history of an article to find out if an edit being considered is a reversion of some prior edit. The rule against reversions applies only to cases where the reverter is aware that the

1272:

I agree. The article is very helpful for someone like myself who is more familiar with statistics and linear algebra than physics. Explaining often mentioned QS concepts in a language that I understand (v. the usual hand-waving with often misleading analogies and examples) gives me a good starting

1049:

The quantum state of a system is a set of numbers that fully describes the quantum system. One typically imagines some experimental apparatus and procedure which "prepares" this quantum state. Quantum states can be statistically mixed, corresponding to a experiment involving a random change of the

711:

Supposing that no one protests, I would also like to update the summary and part of the second section, which are now a bit out-of-sync with the new (first) one. I would also add some details to the last section "mathematical description"; just the reference to "GNS construction" is not quite what

255:

The tautology in the opening sentence here is unfortunate, but mostly unavoidable. If any Wikipedian can come up with a precise, friendly definition of a quantum state, then I'd give them a hearty slap on the back, because the fact is that no such definition exists. Quantum mechanics is somewhat

4309:

Perhaps it is nothing for you to fuss about. On the other hand, usually when I undo mistaken good faith edits, I give a reason on the talk page (unless the edit is obviously mischievous, or a properly adequate reason can fit into the edit summary). I seem to remember that I do that because I read

3791:

To make a definite actual physical entity, a phenomenon, quantum physics requires that both initial and final conditions be determinate. Quantum kinematics defines a quantum 'state' that supplies only the initial, not the final, condition. That enforces its probabilistic character. (Perhaps I may

3453:

You might discuss an edit on the talk page before reverting. But note that Knowledge does not in general require advance approval of edits, and reversions are no exception. If you believe you have an case of an acceptable reversion, you are invited to make that edit unilaterally and if there is

3289:

Looking in more detail. My own personal rule for undoing good faith edits is that by default, such an undo is supported by a careful explanation by the undoer on the talk page. I don't recall where I got that from. If an edit is grossly faulty, then I may depart from that default, and just give a

3065:

I can confidently say that this statement in the intro ("Even in quantum mechanics, for every observable, there are states that determine its value exactly") is erroneous, or at least ambiguous. Does the statement mean "determine value of an observable to an arbitrary accuracy"? If so, it is very

2215:

Thanks for your reply. However, I think the spin is inherent in the specification of been an electron. Is there an electron with spin 3/2? I think we should delete the first paragraph's last phrase about the position or momentum of the electron. I'll send the question to the reference desk to

1974:

I gave the section a bit of a rewrite to clarify some things that seemed wrong or confusing. I removed references to the previous section, the section "The state of a physical system" could be removed as it can be accessed in the history. I will try, later (I'm in work), do some more edits on the

1865:

So sorry not to reply... I’ve been caught up in other pages and not even monitored this one. What you say is clear and correct. It seems the consensus is just to re-write the first couple of paragraphs in the first couple of sections? Trouble is I only know some, not all, of the real meanings and

142:

Unfortunately quantum mechanics is the sort of subject where there is no simpler statement of meaning. Quantum states are mathematical formalities which are manipulated using (more) mathematics to gain information on real-world properties. They are not visualisable phenomena in themselves. As has

4345:

I can see that what I am talking about is not a common subject of discussion here, and so I am asking for a general response before I put up a particular proposal. So far not a word, beyond "I reverted the edit because I found it largely incomprehensible. In addition to the last three paragraphs

3979:

Evidently, Weinberg agrees with the view of Messiah that there are two kinds of object, physical and mathematical. He calls the physical ones "states" and the mathematical ones "vectors" or "wave functions". The mathematical ones "represent" the physical ones. It seems he has important points of

3380:

Don't revert an edit because it is unnecessary — because it does not improve the article. For a reversion to be appropriate, the reverted edit must actually make the article worse. Knowledge does not have a bias toward the status quo (except in cases of fully developed disputes, while they are

3083:

The discussion in sec. 2.7 presenting "statistical" and "mixed" as related concepts appears misleading. "Statistical" relates to ensembles, or at least to a partial knowledge about the details of the state of the system (as in fact noted earlier in sec. 1.1). Non-pure (mixed) state can reflect a

2816:

I have tried to make the lead section clearer and more consistent in physics. Since the lead section tries to run over a lot of ground for the abstract concept which is a lot different from the classical concept, there may still be a few fine points that I have missed. I am not sure which two

2039:

So you deleted it... That’s probably the best move actually, but it did provide analogy with classical mechanics and climaxing with statistical mechanics, to some extent, and statistical mechanics is a good stepping stone towards QM. Anyway the problem of clarification is now over; "if in doubt:

773:

i think you're right. the article agrees with you, except in the intro. it's not clear to me what the quoted statement is saying. in fact, it's not clear at all what most of the introduction is saying. for instance, we have "A fully specified quantum state can be described by...a complete set of

5641:

It is outside my scope to consider such a merge. There is a difference between an inner product and a 'scalar product' as the term is used in the present context. An inner product is between two vectors of the same space. The present 'scalar product' is between vectors from a space and its dual

2840:

The validity of statements like "even pure states show statistical behaviour" depends very much on the assumed interpretation of the "measurement problem" in quantum mechanics. Statements of this kind can only be justified once the framework of ensemble interpretation (or similar) is adopted. A

186:

I dont know a quark about this theme, but I will like to. I think that after this sentence: "A quantum state is any possible state in which a quantum mechanical system can be.", should come a brief explanation about of those possible states or at least some examples. And then the rest: "A fully

4554:

At the same time, a suggestive "physical-like" vocabulary gives the mathematics a liveliness that it would not have if it were just linear algebra. This vocabulary ranges from evocative, to colorful, to confusing, to illusory, and I'm always in favor of clarifying it. And the quantum mechanics

4532:

Still, quantum mechanics has a huge mathematical machine that goes with it. It's out there, and it has to be explained. A lot of it makes very good sense internally, particular when it's just math! As we know the connections with reality are hard to understand. Yet the math is often identified

3958:"The viewpoint of this book is that physical states are represented by vectors in Hilbert space, with the wave functions of Schrödinger just the scalar products of these states with the basis states of definite position. This is essentially the approach of Diracs's ″transformation theory″."< 3578:

In ordinary language, that comment is right in saying "A state is how something is." The rest of the comment is more or less about the term of art 'quantum state', not about ordinary language. By default in Knowledge, ordinary language has priority. The Copenhagen interpretation, insofar as it

1997:

Good effort! Though it may be better to change the description slightly along these lines: rather than say "we push on the particle with speed", its more accurate to say "an external agent moves the particle with a definite momentum (and hence speed)", since there is a more direct statement to

1909:

It seems to me that some people regard the state as something that is really there and that experimenters are trying to describe accurately, but that for other the state is the abstraction that has some tentative relationship to reality, i.e., the state is a mathematical model or a "convenient

3776:

between the system and certain apparatus of entirely classical (i.e. directly controllable) character which serve to fix the conditions of observation and register the results. A phenomenon is therefore a process (endowed with the characteristic quantal wholeness) involving a definite type of

1591:

it appears to me that the intent of the writer was to speak from the standpoint of classical physics and maintain that there are real facts about the universe that include P at time t and Q at time t that (measurable =) can be measured—assuming that we do things right. Getting some reasonable

762:

The intro states, "For example, in the case of a single particle in a one dimensional box, the state of a particle can be defined by a single quantum number related to the energy of this particle." A general quantum state is a superposition of every energy eigenstates, each with a potentially

4852:

It is not easy to find the perfect word for where I have written 'designated'. Other candidates might be 'symbolized', 'formulated', 'denoted', 'presented', 'signified', 'expressed'. Dirac writes "In the accurate mathematical theory each translational state is associated with one of the wave

789:

Now for the quantum numbers: What physicists mean here is a label for a basis in the Hilbert space. The link is as follows: Pure states correspond (more or less) to vectors in the Hilbert space. It usually suffices to consider a basis (often, the basis of eigenstates of the energy operator).

3025:). Also, let's remember the talk page is for discussing the content of the article, not chatting on the topic. If you think there's a fundamental flaw in a highly cited RMP review, why don't you find a reliable source that disagrees with the above (rather weakly phrased imho) statement? 1026:

I think it's on the right track, but I wish there was a better first summary sentence than "a complete description of the parameters of the experiment". When I read this I think, "okay, a quantum state is how much liquid helium I put into the dewar, what brand of monochrometer I'm using,

4165:

A physical entity can be directly manipulated or observed empirically as it manifests itself in a phenomenon, but this is not true of mathematical entity. A phenomenon can be uniquely identified by the time and place of its occurrence, but this is not true of a mathematical entity.

4327:

I think until there is an acknowledgement here that there was a breach of proper behavior, I would be inviting more breaches if I knuckled under, and did what I was bid. It seems, with some latitude of reading, you are continuing the pattern by suggesting that I should I knuckle

203:

that weren't as circular as that sentence! "In quantum mechanics, a quantum state is any possible state in which a quantum mechanical system can be." Well, that clears it right up. Gee, thanks. And I suppose the science of physics is the branch of science that deals with

4686:. Further, the last stage of the "preparation" can be the passage of the mixed beam through a specially suitably chosen physical object, such as for example a Stern-Gerlach spin-analysing magnet, and the selection of just one of its output sub-beams. Such a sub-beam is in a 4578:

It would add greatly to the comfort of other editors if you would very kindly be willing to choose for yourself a suitably non-identificatory User name and routinely use it. I feel uncomfortable chatting with a number. I think a user name does not create a security problem.

1152:, the quantum state of a system is a mathematical object that fully describes the quantum system. One typically imagines some experimental apparatus and procedure which "prepares" this quantum state; the mathematical object then reflects the setup of the apparatus. (...) 4455:

of an isolated system of one or more particles." A simple-minded reader of Knowledge might presuppose that a wave function was a mathematical entity that describes a physical entity called a quantum state. Then he might follow the link and arrive at the present article

3211:

to the policy page. Dated 02:11, 331 August 2014, it changes the wording "With large proposed deletions or replacements" to "major change". That makes it a major change, because the context is that changes are of three kinds, addition, deletion, or replacement. I found

2411:

of an oversimplification than mentioning the position in that sentence. I do think that spin should be mentioned in the first few sentences, as the main difference between the technical terms "quantum state" and "orbital" is that the former but not the latter considers

3768:. .... The wholeness of quantal processes necessitates a revision of the concept of phenomenon. Since the concepts which in classical theory describe the state of a physical system are actually subject to mutual limitations, they can no longer be regarded as denoting 1325:. Briefly, the reader needs to know why a basis is needed (states are vectors), that the basis states compose non-basis states through linear combination, & the bra-ket notation for composing a state from the basis states. If my thinking's solid, the formula from 5372: 3180:, because on Knowledge a lack of information is better than misleading or false information—Knowledge's reputation as an encyclopedia depends on the information in articles being verifiable and reliable. To avoid such challenges, the best practice is to provide an " 1211:

Ah! Now I see what you meant - I was reading the word 'results' as a verb and you were using it as a noun - lol - sorry. Maybe use 'the results of measurements of pure quantum states' instead - and its not a minor point, that is important to keep clear. Go for it!

3336:

Whenever you believe that the author of an edit was simply misinformed, or didn't think an edit through, go ahead and revert. If that editor (or anyone else) re-reverts, you'll know it's more than that and can be more conservative in deciding whether to revert it

4266:

put up with the possibility that they might be undone by someone else. (I agree that generally one should give reasons when reverting, but some people think it's enough to wait until asked "why?" before giving their reasons - it's probably nothing to fuss about.)

2871:

Maybe 'the above example' is ill defined but the given wave function, a bell basis state, is maximally mixed and thus the opposite of pure. The state vector of a hydrogen energy spectrum is pure though, so maybe that is what is referred to. (by Physics Grad Stud)

5074: 4176:

Ultimately, you could insist that this distinction is meaningless or nonsensical. Then I would say that articles about physics in Knowledge would often be puzzling or uninteresting for you. I think the distinction is sound and necessary for an understanding of

1597:

At this point I have one foot on the dock and the other foot on the rowboat. Assuming that the above part is correct, then the rest of it would mean that future measurements can be predicted. But in that case it would seem to me that the sentence should have

4837:

Dirac writes in his preface "For this reason I have chosen the symbolic method, introducing the representatives later merely as an aid to practical calculation." It could confuse a new reader to find the word 'represent' used in the lead as it was till now.

4250:

Putting my question again here, in a simile, I am asking, is a quantum state like a football match (physical entity), where one goes and encourages one's team, or is it like a newspaper report of the match (mathematical entity), which one reads at home next

4128:

widely quoted on the subject of quantum mechanics, and exploring his views I find that Bohr's mature view put the notion of a 'quantum phenomenon' as more or less primary and fundamental; but I find no page with that heading. When I go the article entitled

619:

I'm not a total science person, but I know enough to know that they should probably be kept seperate. I think the beauty of wikipedia is to have as much detail as possible on different pages. As long as the topics are well-linked, the info is accessable.

4049:

Evidently, for Wheeler and Bohr, a quantum mechanical phenomenon is an actual physical entity, a fully determinate process, with a finite time duration, with no remaining unrealized potential possibility. Such is not a quantum state as defined by Dirac.

2455:

If we give an example in the first paragraph, it ought to be a simple and well-thought-of example, otherwise, we would spend a lot of time covering all the strange cases. Thus, I propose to change the first paragraph of the lead section to as follows:

137:

The page as it stands gives only an old-fashioned Copenhagen-like account of measurement, which by itself is incomplete and unsatisfactory since it doesn't describe what constitutes a measurement and how the system interacts with what's measuring it.

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facts about the thing being measured. In other words, I am guessing that those capital letters refer to the realities that experimenters are trying to measure. But whoever wrote the sentences in question should be the one to help straighten things

1226:"In quantum physics, a quantum state is a mathematical object that fully describes a Quantum system" Ok, I am a lay person and am not sure if I am understanding this correctly. Is a quantum state a mathematical object or a condition of nature? 5205: 158:

I'm no expert but I think this sentance "Doing this, we determine the initial position q and the initial momentum p" seems to contradict the heisenberg uncertainty principle, that we cannot know the position AND momentum at the same time.

4385:, a fair writer to quote here, "It is only too true that, isolated from their physical context, the mathematical equations are meaningless, but if the theory is any good, the physical meaning which can be attached to them is unique."< 3163:

add information to Knowledge, either by creating new articles or adding to existing articles, and exercise particular caution when considering removing information. However, it is Knowledge policy that information in Knowledge should be

3582:

The quantum state is a fundamental conceptual element of quantum mechanics. Failure to define it well here makes for slippery, muddy ground for all other articles on aspects of quantum mechanics. It would be good to do it right here.

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I suggest that the article should significantly expand on the concept of "state" in a sense that it is a description of a system which disregards previous history of the system, perhaps making a connection to Markov processes.

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They could, however, be mentioned in full in the subsequent section on spin states. (To really treat it in full, you also need to specify the spin state for both the electron and the proton, rather than just the total spin).

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There are a lot of other unclear places. For example, what is the status of an eigenstate. Why should they exist ? Are they only mathematical objects or there is a fundamental low of the nature that guarantee their existence ?

4025:"Had quantum mechanics stopped here, its deepest lesson would have escaped attention: ″No elementary quantum phenomenon is a phenomenon until it is a registered (observed) phenomenon.″"<Wheeler, Zurek (1983), page xvi.: --> 3668:

It seems that Born thought of ascertained results of determinate physical processes in terms of probabilistic successions of jumps between quantum states as physical objects that correspond with mathematical entities called

3322:

In the case of a good faith edit, a reversion is appropriate when the reverter believes that the edit makes the article clearly worse and there is no element of the edit that is an improvement. This is often true of small

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We speak of a (spinor-valued) wave function from R^3 to C^(2S+1) in the first sentence. We speak of a (complex-valued) wave function from {-S,...,S} x R^3 to C, in the second sentence. Remarkably, these are equivalent.

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It has been remarked that this article was very technical. I have tried to fix this by adding a "conceptual description" that includes only minimal technicalities. The drawback is that the article is now rather lengthy.

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one significant element of the edit, it is not a reversion. If a supporter of the reverted edit wants to save more of it, she can re-edit in smaller pieces and the article can converge on a consensus version that way.

654:

I added a link to NASA to the excited state page to help make the information a little more user-friendly. That might also be a good base reference for anyone who wanted to make the wikipage more basic/complete.

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describing the measurement. However, unlike in classical mechanics, even the measurement of pure quantum states is only determined probabilistically. This reflects a core difference between classical and quantum

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5255: 785:

I agree, the introduction needs to be rewritten. In general the link between the physical concepts and the mathematical objects is not really well explained. I really need to add that "Mathematical formulation"

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At the outset it could be made clear that this is a mathematical description using statistics to describe experimental results. It should not be confused with being an actual representation of anything real.

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The main purpose of reversion is to undo vandalism. If you see an edit that you're sure was intended by its author to damage Knowledge, and it does, there is no need for further consideration. Just revert

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fundamental quantum-mechanical uncertainty: the entire system can be KNOWN to be in a particular well-defined pure state, yet its subsystem is in a mixed state. Yes, the same density matrix formalism can be

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As I read this, Messiah has in mind two entities, a physical object in a quantum state, and a mathematical object that lives in a function space. He thinks the mathematical object "represents" the physical

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These seem like very interesting content. Perhaps we can have a section just for the bound states and unbound states of the hydrogen atom. Hopefully, someone familiar with atomic physics can provide more

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Could someone who knows enough about it please add something about the quantum state necessary for antimatter and matter to annihilate with each other when they come into contact with one another? Thanks!

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My knowledge is quite shallow here. I was thinking of something like the observer being part of the observed system, but I guess there would be nothing to be called a "measurement" then. Skimming through

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I think there is significant Wiki edit confusion in this article, not entirely a feature of the field. The best writers acknowledge that physics and mathematics are distinct and need explicit linking.

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remark that Einstein was not sure that Nature works by preparing pure states and detecting final states as required by quantum mechanics. Indeed, it is obvious that Nature supplies only mixed states.)

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is incorrect; since the example is within classical physics P(t) and Q(t) do represent the specific results they produce in a certain run of the experiment presuming experimental error is eliminated.

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have degenerate eigenvalues, you need to add other labels to distinguish the basis vectors (example: the eigenvalues of the angular momentum operator), that leaves you with a "set of quantum numbers".

2158:. This wave function can give hydrogen's probability density in position space and momentum space. So, what other information about the position or momentum of the electron are not specified?-- 190:

I agree about the first sentence mentioned above: the opening sentence of the article seems tautologous, and it doesn't become clearer until one reaches the Superposition and Pure/Mixed sections.

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if it does get fleshed out, perhaps a good remark to include would be that, given an algebra of classical or quantum observables, a physical state is a positive linear functional on the algebra.

3764:"It is only too true that, isolated from their physical context, the mathematical equations are meaningless: but if the theory is any good, the physical meaning which can be attached to them is 5280: 3467:

You could also discuss an edit directly with the editor who made it, on that editor's talk page, and request that the editor modify his own work. Or convince you that it's best as it stands.

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the function of position in a classical treatment. Classically, the initial state, i.e the values of P(0) and Q(0) determines the future evolution of the system exactly. The line that reads

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the electron are entangled with each other (spin-orbit coupling), and with the photon field (cf spontaneous emission) :-) So I am not convinced that mentioning the spin in that sentence is

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directly with the physics. This is a feature of the field, not of Knowledge editors. Since the correspondence is very non-local, this tends to pull the physics over into the mathematics.

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different complex coefficient, so the state characterized only by an infinite sequence of complex numbers, right? Or am I misunderstanding how the term "quantum state" is being used? --

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into the same article. (I think if you want to suggest any of those mergers, then you have to do all of them). On the other hand, I think it's too much to merge it into this article (

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The "quantum state" is defined in terms of the "quantum system", but when you follow that link, it takes you to the "Quantum Mechanics" article, which does not define "quantum system".

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The link for "Quantum system" actually delivers the user to "physical system," and that article does not say anything about a quantum system as distinguished from a classical system.

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There are a couple of ambiguities earlier in this article. I think they are simply English-writing ambiguities. If I fixed them wrong, then some deeper examination needs to be done.

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be read either as a scalar product between two vectors of the same space, or as a functional acting on a vector, but never as a scalar product between a functional and a vector?

2338:, and this specifies four properties (The principal quantum number: n, The azimuthal quantum number: ℓ, The magnetic quantum number: mℓ,The spin projection quantum number: ms ). 1930:

An alternative to re-writing the paragraph would be to mention the classical analogue as required in the prose of the section that follows it. I wouldn't mind giving it a stab.

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Electrons have spin 1/2. I'm not sure what issue with the first paragraph that you are referring to. If you want more opinions related to the article try wikiproject physics.

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Yes - that user should, but what is the chance (excuse probability/QM pun) of that occurring? All we can do is wait for someone from the wikiproject talk page to reply...--

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My reading of the above leads me to think that it was improper that my edit was undone without the undoer giving reasons on this talk page; an edit summary was not enough.

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The page is nice but it's a bit too technical for non-physics (like me!). Can it be rewritten with more user-friendliness, without perhaps sacrificing completeness?

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An example of a physical entity is the activity of the monitor on which you are now reading this sentence. An example of a mathematical entity is a cardinal number.

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was of the kind 'adding information', which is covered by explicit policy advice to be bold, not of the 'deletion' or 'replacement' kind, for which caution is urged.

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Here P(t) and Q(t) refer to the measurable quantities (observables) of the system as such, not the specific results they produce in a certain run of the experiment.

4912: 4873: 2601:{\displaystyle \left|\psi \right\rangle ={\frac {1}{\sqrt {2}}}{\bigg (}\left|\uparrow \downarrow \right\rangle -\left|\downarrow \uparrow \right\rangle {\bigg )}} 991:

is really bad, imprecise, and highly misleading language. i'd be surprised if that's common physicist's jargon. if it is, i suggest it be not used in the article.

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are now quite different articles, neither one being very short, and both covering their own material in their own sort of way without that much overlap. However,

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I think it would be fair to say that Rosenfeld was a respected supporter of the Copenhagen orthodoxy, without committing oneself to exactly what that might mean.

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I'm afraid the above guesswork is not very useful. It might result in correct sentences but obscure the intended, and more salient, meaning originally intended.

2480:. The state vector theoretically contains the most information possible about the quantum system. For example, when dealing with the energy spectrum of the 1258:

I just read about 80% of this article. It is understandable and accessible. To those who worked to make this article accessible and understandable - Good job!

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I have written "may be designated" because there are other important ways of presenting states, such as explicit wave functions, and elements of a C* algebra.

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fiction" and nothing more. I believe this difference in opinion (or interpretation) must apply to the whole article and not just to this one small part of it.

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Perhaps you didn't read the statement carefully enough? I think you know how to project a Dirac function on the base kets (but if not you can read about it

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This formulation has been around for quite some time. If it doesn't mean anything useful to anybody now involved, maybe the best thing to do is to delete it.

4195:, I'm afraid I'm having a hard time following you here. Could you perhaps post a wording that you think would be better so we can look at that? Thanks, 3051:. Is a “non-normalizable state” a quantum state? Or it is a supplementary construction? At last, can anybody say what exactly did L. E. Ballentine write? 1173:

I like the "mathematical object that fully describes the quantum system" part - much nicer. The second recommendation though doesn't work grammatically.

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I think this is an improvement on what is there - I like it. I particularly like the statement about the apparatus and procedure that prepares the state.

515:- Quantum state is a specific universe of physics theory. Excited states exist in classical mechanics and thermodynamics. A merger would be nonsense. 3395:

favor of the status quo, so your finding that the article was better before might just be a result of that. Also, Knowledge likes to encourage editing.

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There are chiefly two very different interpretations when dealing with the concept of state vector. One is the statistical interpretation advocated by

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to visualize it, and only its result can be ascertained. This result is, that after the jump, the system is in a different quantum state. The function

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first, technical aspects later. It's extremely frustrating to see mathematical or physics wiki articles that begin with technical jargon. Well done.

5622::D I don't think so, your sourcing is clear. But that means that the "scalar product" from all these citations is actually described in the article 967:

the quantum state of a system is a set of numbers that fully describe a quantum system. ...These numbers are called the quantum numbers of the system.

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Near the beginning there are two sentences beginning with a bold-face A. The text shouldn't take this form, but I can't see where the problem lies. "

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quantum state is a specific universe of physics theory. excited states exist in classical mechanics and thermosdynamics. a merger would be nonsense

1496:) refer to the measurable quantities (observables) of the system as such, not the specific results they produce in a certain run of the experiment." 948:

In short, the intro needs a rewrite and I didn't do that when I found the article and added the "conceptual introduction"... But maybe I should. --

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the most information possible about the quantum system. For example, the state vector of an electron within a hydrogen atom is given by its four

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A quantum state of a system is typically generated by some experimental apparatus and procedure which "prepares" it.<Ludwig, G. (1954/1983).

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One typically imagines some experimental apparatus and procedure which "prepares" this quantum state. Quantum states can be statistically mixed

4480:." He might think 'this is odd, it looks like another mathematical entity, not a physical entity after all'. Does he deserve some help in this? 2966:

context) and had his textbook printed on paper afterwards. If he did, then he should be disqualified because only an operator with a non-empty

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I’d wonder if Mr. L. E. Ballentine really said that “for every observable there are states that determine its value exactly” (outside a finite-

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momentum and is more formal. Then again, its supposed to be explained as plainly as possible for the average reader. Thanks for your help =) --

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A reader might come to this article thinking it would be about physics. No, it is about mathematics. The first sentence tells me it is about

3970: 82: 5542:(2009). Ballentine (1998) sees 'inner' and 'scalar' as alternatives. Beltrametti and Cassinelli (1982) speak of the "scalar" product. As do 2705:

states of one proton and one electron (if one ignores the location and motion of their center of mass) can be associated with a five-tuple:

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articles are hard to read because they add layer of Wikifog to the usual confusions. For me the broadness of perspective makes up for this.

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of 'undisturbed'. An indeterminate state does not define a physical phenomenon, such as is intended by Wheeler in his well-known aphorism

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The changed statements are supported by referenced textbook. If nobody disagrees, I shall proceed to edit with the above modification.--

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specified quantum state can be described by a state vector, a wavefunction, or a complete set of quantum numbers for a specific system."

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In the olden days they tried to define their terms. Kramers distinguished the physical situation from its mathematical characterisation.

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Knowledge is here to provide information to people; generally speaking, the more information it can provide (subject to certain defined

3099: 2873: 1514:?) and not the continuous variables which are measured in an experiment, but then it says "measurable (observables) of the system", why? 417:

should not be merged. There is simply too much to say about calculation of energy levels. So I guess I'm left considering a merger of

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is usually called the wave function of the stationary state, although the true wave function differs from the latter by a phase factor

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is a more appropriate term, because it generalizes the scalar product to abstract vector spaces over (possibly complex) fields. The

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determines the transitions in the following way: every state of the system corresponds to a particular characteristic solution, an

462:). I don't see a problem with merging those here, its not that much info. And, they all fall under the category of quantum states. 5383: 4638: 2194: 1079: 1059: 5081: 4124:. You may care to look at that article. I think perhaps you will thereupon be appalled. Or perhaps not? In the literature I see 2923:

The lead says that the quantum state has to be a vector, but as far as I'm aware that's just one way to encode a quantum state.

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0, we conduct measurements on the particle. The measurements we can perform on this simple system are essentially its position

4460:, expecting to find that it is about a physical entity. He would read the first two sentences of the lead of this article: "In 3044: 1242: 3381:

being resolved). In fact, Knowledge has a bias toward change, as a means of maximizing quality by maximizing participation.

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a "quantum number". If the energy operator does not have degenerate eigenvalues, you can take its eigenvalues as the label

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in particular is a trivial subset of the quantum states - and could easily be a simple section on this page. Any comments?

130:

It would really be nice to see some more on what quantumphysical characteristics of particles define their quantum states.

5367:{\displaystyle \langle \mathbf {r} |\mathbf {r'} \rangle =\mathbf {r'} (\mathbf {r} )=\delta (\mathbf {r} -\mathbf {r'} )} 667:(?) are based on the quantum state of the system and the quantum operations acting on the state. ": it is not clear to me. 3268:

replacements", as they did prior to the "tightened wording". I assume that Knowledge policy is consistent, more or less.

2085:

I'm still planning to go over it again and provide some form of analogy but I think in the interim it is best left out.

66: 4833:'represent' has a special technical meaning in this topic and the word is not suitable for its former place in the lead 396:

Sounds like a good plan. I don't know when i'd get to doing that tho. I'll try to start a merge of some of those soon.

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Knowledge, one needs to try to put it into words, and one needs to be and can expect to be partly successful in that.

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I personally do not mean anything by the two letters. However, I am guessing that they were intended to represent the

5765:) Isn't a 1928 article too old to dispel concerns about alternative interpretations, which could be proposed later? 5069:{\displaystyle \mathbf {r} _{1}\neq \mathbf {r} _{2}\Rightarrow \langle \mathbf {r} _{1}|\mathbf {r} _{2}\rangle =0} 2801:

mixed state..." It looks like something might not have been terminated earlier. Strange behavior. Can anyone fix it?

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to refer to observations obtained under specified circumstances, including an account of the whole experiment."<

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Consider a system with just 1 hydrogen atom. The wave function for the electron only requires 3 quantum numbers

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Some time ago I posted on this page some views from respected sources about what is a quantum state? No response.

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An acknowledgement that there was a breach of proper editorial behaviour would be a step in the right direction.

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How should this article define the term 'quantum state'? Below I will offer some findings from reliable sources.

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A fully specified quantum state can be described by ... a complete set of quantum numbers for a specific system.

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decipher the wording to get to the meaning behind it. Ambiguous, careless, unclear, even illogical. Hopeless.

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It's unclear to me what's wrong with the statement, since it seems equivalent to how observables are defined.

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The statement was written in 2007 and the editor who wrote it has not been active since 2010. No use waiting...

1358:= 1 that moves freely, and without friction, in one spatial direction. We put the particle at initial position 1326: 1063: 704:

Maybe there are still some aspects missing (due to brevity). Maybe parts of that description might be moved to

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pretty much covers their most important material anyway. I think I'll make a note of this potential merger of

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is right. We should primarily use secondary sources and secondarily primary sources. Optimally, we have both.

2908: 2887:"Mixed states" and "entangled states" are not the same notions. A Bell state is pure and maximally entangled. 2856: 2625:, among others. It proclaims that quantum state can completely describe the quantum system under examination. 5510:

would have a fair chance of being a reliable source on this topic. As cited, he says "scalar product". So do

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I don't think, however, that I've changed any substantial underlying priciples of this policy as a whole. --

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that were perhaps a better choice for handling ideas in transformation than prematurely frozen mathematics.

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disagreement, you'll find out from subsequent edits. (But note the special rules for avoiding edit wars).

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section "Quantum states" to sum up any relevant points from the section "the state of a physical system".

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functions of ordinary wave optics." In the present article one finds "pure quantum states correspond to

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you are trying to add to the article, and maybe we can work together to draft a better version? Thanks

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Note that the talk page is for making improvements to the article. For questions about the physics, try

2163: 1366:= 0 by pushing the particle with some speed and in some direction. Doing this, we determine the initial 1238: 623: 602: 4841:

I have replaced the former sentence with "A pure quantum state may be designated by a vector, called a

144: 4861:." I think 'designated' may be the best option where I have used it. Perhaps "corresponds" is better? 4116:. There I find that quantum mechanics "deals with physical phenomena". When I follow the lead link to 5852: 5848: 5783: 5779: 5756: 5726: 5722: 5647: 5643: 5605: 5601: 5471: 4908: 4904: 4869: 4865: 4812:

variable (for the spin) is added to the usual three continuous variables (for the position in space).

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I agree that this article is unclear. It certainly didn't give me the information I was looking for.

104: 3022: 272: 5798: 4708: 4134: 3883:"A physical situation which is characterised by a solution of the Schrödinger equation of the form 3603: 2737: 2441: 2235: 2202: 2090: 1980: 1935: 1855: 1338: 1234: 4645:, and the form that this distribution takes is completely determined by the quantum state and the 4389:(1957), Misunderstandings about the foundations of quantum theory, pp. 41–45 in editor S. Körner, 2042: 2000: 1868: 1809: 1723: 1655: 1550: 1385: 1066:, and the form that this distribution takes is completely determined by the quantum state and the 793: 458:, but I don't think there's a good way of merging excited state as well - unless its merged here ( 3225: 2802: 1953: 1911: 1776: 1696: 1624: 1318: 1300: 1217: 1197: 1178: 1159: 1104: 1005: 949: 716: 320: 47: 17: 5721:

By the mathematics books, you have to be right. But the context is physics as found in sources.

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As I read it, Knowledge posts what reliable sources say, in context. The sub-section is headed

5200:{\displaystyle \int \langle \mathbf {r} '|\mathbf {r} \rangle \mathrm {d} ^{3}\mathbf {r} '=1,} 626: 236:

This article is the most impenetrable I've ever seen on Knowledge, and that's saying something.

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Now, when I try to 'discuss on talk page before adding', I am asked to add before discussing.

3691:"As a more appropriate way of expression, one may advocate limitation of the use of the word 3088:

to describe statistical uncertainty, but this does not mean that the nature of a mixed state

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function as a "set of numbers" seems like stressing the picture too far.) How about this one:

5584: 5378:(with slight stretching of notation in the second step). This can be motivated by demanding 4766:

Ballentine (1998) pp. 47–48, as I read it, says no such thing. The reference was introduced

4621:"The quantum state of a system is a set of numbers that fully describes the quantum system. 4200: 3506: 3177: 3052: 3030: 3008: 2990: 2971: 2932: 2818: 2772: 2752: 2690: 2675: 2393: 2373: 2217: 2159: 1263: 598: 463: 455: 418: 397: 376: 356: 346: 216: 1866:

implications of quantum states inside-out (yet)... else it would have been done by now...--

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entity, though it may be true of an abstraction that refers to actual physical entities.

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The logical structure of the article has, in my opinion, not improved since that comment.

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for a long time, it's not your fault.) This could be fixed with a small wording change. --

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http://en.wikipedia.org/search/?title=Quantum_state&direction=next&oldid=128407213

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Please comment. Hopefully, the article's lead section can be improved further, thanks!--

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There are a number of things that sometimes motivate an editor to revert, but shouldn't.

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Fine for me in principle, but I disagree with the "set of numbers". (Describing e.g. an

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is the unit operator (completeness relation). I think that this should rather go into

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in effect undone a fair post by me. He made no edit summary and no talk page comment.

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for instructions on how to do this, or ask for assistance on the article talk page)."

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approximation of "right" involves "specific results" in many "run of the experiment."

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corresponds to a well defined energy of the system under consideration is called a

3870: 3801: 3722: 3678: 3532: 3510: 3492: 3284: 3252: 3197: 3181: 3173: 3130: 3107: 3060: 3034: 3016: 2994: 2979: 2951: 2936: 2912: 2896: 2888: 2881: 2860: 2826: 2810: 2780: 2760: 2741: 2473: 2445: 2431: 2397: 2381: 2266: 2239: 2225: 2206: 2186: 2167: 2094: 2064: 2022: 1984: 1961: 1939: 1919: 1890: 1859: 1831: 1784: 1745: 1704: 1677: 1632: 1572: 1342: 1308: 1288: 1267: 1246: 1221: 1205: 1182: 1167: 1108: 1091: 1013: 995: 992: 952: 778: 775: 767: 749: 730: 727: 719: 685: 671: 641: 606: 590: 582: 578: 574: 566: 562: 550: 538: 519: 495: 487: 466: 433: 426: 414: 400: 387: 380: 368: 360: 349: 334: 323: 308: 297: 280: 219: 174: 147: 116: 90: 307:(or of the interaction of the system, if you like), not of the quantum state. See 3263:

Assuming that Knowledge policy is more or less consistent, the above quote about

5258: 4770:. I have therefore deleted the reference. Perhaps a relevant on will be offered? 4724: 4411:

I ask my question again, is a quantum state a mathematical or a physical entity?

4196: 4144:

is near-enough nonsense, how is the reader to approach the rest of the article?

3781:(1957). Misunderstandings about the foundations of quantum theory, pp. 41–45 in 3502: 3165: 3026: 2986: 2928: 2389: 1259: 668: 638: 516: 492: 312: 46:

If you wish to start a new discussion or revive an old one, please do so on the

1438:

is momentum, and these are continuous variables which can take any values, and

5507: 4794:

As a consequence, the quantum state of a particle with spin is described by a

4646: 4130: 4125: 3696: 3293:

In more detail of policy (I don't want to be a Wikilawyer) I find on the page

2679: 2622: 2515: 1067: 4625:, corresponding to a experiment involving a random change of the parameters. 4975:{\displaystyle \psi (\mathbf {r} )\equiv \langle \mathbf {r} |\psi \rangle } 2817:

sentences are giving you problems. It would be nice if they can be fixed.--

1058:

which cannot be described as a mixture of others. When performing a certain

2249:

I propose to change the first paragraph of the lead section to as follows:

1373:

of the particle. These initial conditions are what characterizes the state

4391:

Observation and Interpretation: a Symposium of Philosophers and Physicists

3633:, of the differential equation; for example the normal state the function 715:

In my opinion, the "concept" template can be removed now. Any opinions? --

3652: 2481: 1848:

not the specific results they produce in a certain run of the experiment.

1807:

You raise a good point, and may be correct about deleting. Shall we?...--

1367: 3172:. You are invited to show that information is verifiable by referencing 2771:

If everyone agrees to the proposed changes, let me give it a try then.--

4033:

Here Wheeler is referring to statements such as the following by Bohr:

4010:, fourth edition, Oxford University Press, Oxford UK, pages 11–12.: --> 3930:, translated by D. ter Haar, North-Holland, Amsterdam, pp. 58–59.: --> 2608:

involves superposition of joint spin states for 2 different particles.

549:, particularly electron quantum states. I have recently expanded the 2488:, the relevant state vector is given by the principal quantum number 1158:"measurement results in pure quantum states" in the last sentence. -- 4613:

a section that I regard as a good description of a physical entity

2927:

are also used to represent quantum states. Am I wrong about this? --

1526:, i.e. the results that our measurements will produce, depending on 4140:

Finding that the first sentence of the lead of the present article

5250:{\displaystyle \langle \mathbf {r} |\mathbf {r} \rangle =\infty .} 5126:

It seems that the normalization condition has to be replaced with

3739:(1927). The physical content of Quantum kinematics and mechanics, 1321:

is red. It's probably more appropriate to explain it here than at

2728:

How does one extend this to a complete basis which would include

5583:

Some authors who do not use the Dirac bra–ket notation, such as

3772:

of the system. Their true logical function is rather to express

3121:

a good faith edit was undone without comment on this talk page.

3745:: 172–198, translated in Wheeler, Zurek (1983) pp. 62–84.: --> 3043:

intervals virtually explicates a homebrew idea similar to the

2999:

Lolwut? Consider a particle on the line, or on the circle, or

1354:"Consider an experiment with a (non-quantum) particle of mass 1004:

I rewrote the lead paragraph now. Comments are appreciated. --

25: 5425:{\displaystyle |\mathbf {r} \rangle \langle \mathbf {r} |=I,} 3814:"When the system is in a state represented by a wave of type 4641:

on a quantum state, the result is in general described by a

3003:. Which quantum state “determines exactly” the value of the 1062:

on a quantum state, the result is in general described by a

5642:

space; these two spaces in the present case are isomorphic.

5115:{\displaystyle \langle \mathbf {r} |\mathbf {r} \rangle =1} 4896:, 4th edition, Oxford University Press, Oxford UK, p. viii. 2173:

Those three quantum numbers do not say what the electron's

1157:

Also, I suggest "measurement of pure quantum states" -: -->

4747:

That's what I mean by physics as distinct from mathematics

4054:'state' and a classical ordinary language physical state. 1649:. So we are both confused? This should be notified at the 4690:

with respect to that analyser, and can be described by a

3699:(1948). On the notions of complementarity and causality, 2919:

wave functions are also representations of quantum states

2216:

make sure the lead section shows the accurate physics. --

4739:

This is why quantum mechanics is a probabilistic theory.

4232:

I am having a hard time seeing how one must behave here.

3908:

and which thus in accordance with the quantum postulate

3543:

How should this article define the term 'quantum state'?

3114:

Good faith edit was undone without talk page explanation

341:

with this page. They are all very related concepts, and

5844: 4767: 4602: 4081:

is a quantum state a mathematical or a physical entity?

3548: 3272: 3246: 3213: 3208: 3118: 2642:(2nd, illustrated ed.). John Wiley & Sons. p. 166. 2355:(2nd, illustrated ed.). John Wiley & Sons. p. 166. 1767: 790:

Mathematicians would write the basis as something like

413:

Looking at the articles, I've come to the opinion that

3850:, volume 1, translated by G.M. Temmer from the French 3777:

interaction between the system and the apparatus."<

3216:

about it on the relevant talk page. The comment reads

2903:

Thanks! I really need to get my definitions straight.

1188:

Well, what I wanted to point out is just that not the

5835:

edit undone without edit summary or talk page comment

5662: 5386: 5283: 5216: 5136: 5084: 4994: 4935: 2664:"The Statistical Interpretation of Quantum Mechanics" 2528: 2494: 2286: 2119: 1388: 1120: 927: 907: 880: 850: 829: 796: 5530:(2013) also speaks of the "scalar product", as does 3049:

they… do not represent physical states of a particle

4393:, Butterworths Scientific, London, on page 41.: --> 3551:. To make it easier to discuss it, I copy it here: 1050:parameters. States obtained in this way are called 5682: 5600:Perhaps a further survey of sources may be needed? 5424: 5366: 5249: 5199: 5114: 5068: 4974: 4924:Quantum state#Basis states of one-particle systems 2600: 2506: 2330: 2150: 1412: 1133: 933: 913: 893: 864: 835: 815: 5591:(1949), though not Weinberg, use "inner product". 4635:which cannot be described as a mixture of others. 4085:I read the lead's first sentences telling me "In 3785:, edited by S. Körner, Butterworths, London.: --> 3241:I guess I will take the policy's own advice, per 2942:Wave functions are vectors in a Hilbert space. -- 2593: 2557: 1548:Does anyone know what the section tries to say?-- 1040:I'm thinking, maybe something along the lines of, 4707:A quantum state is characterized by its quantum 4364:to question whether more detail would be useful. 1610:", and not "depending on future observations of 1428:of the system by fixing its initial conditions." 4673:, translated by C.A. Hein, Springer, New York, 4601:Glancing at a place above on this page, I find 3655:(1927). Physical aspects of quantum mechanics, 5559:Robinett (2006) mixes Dirac notation with the 4443:, I read the opening sentence of the lead: "A 3176:. Unsourced information may be challenged and 1524:value of the observables in the specific state 4658:Here is a modified version of the foregoing. 4472:. A quantum state is given as a vector in a 4097:. A quantum state is given as a vector in a 3547:I find an unsigned IP edit to this talk page 3184:" at the time the information is added (see: 8: 5677: 5663: 5400: 5397: 5307: 5284: 5235: 5217: 5163: 5140: 5103: 5085: 5057: 5025: 4985:does not work for orthonormality conditions 4969: 4953: 3966:, Cambridge University Press, Cambridge UK, 2701:Each vector in one particular basis for the 2640:Quantum Mechanics: Concepts and Applications 2501: 2495: 2353:Quantum Mechanics: Concepts and Applications 2325: 2287: 2145: 2120: 1506:? Based in this description they are simply 810: 797: 5683:{\displaystyle \langle \phi |\psi \rangle } 3047:, and finally (after 13.67) concludes that 2331:{\displaystyle \{n,\ell ,m_{\ell },m_{s}\}} 2273:. The state vector theoretically contains 2958:Do eigenstates exist for every observable? 2836:Strong implicit interpretation assumptions 1641:I still don't understand what you mean by 1442:is just the state, the 2-tuple containing 941:("the energy as a quantum number"). If it 774:quantum numbers...". what does that mean? 573:are rather short and could be merged into 329:Merge with excited state, and Energy level 5669: 5661: 5408: 5403: 5392: 5387: 5385: 5351: 5343: 5326: 5313: 5297: 5292: 5287: 5282: 5230: 5225: 5220: 5215: 5179: 5172: 5167: 5158: 5153: 5144: 5135: 5098: 5093: 5088: 5083: 5051: 5046: 5040: 5034: 5029: 5016: 5011: 5001: 4996: 4993: 4961: 4956: 4942: 4934: 3854:, North-Holland, Amsterdam, page 72.: --> 2592: 2591: 2556: 2555: 2543: 2527: 2514:. For a more complicated case, consider 2493: 2319: 2306: 2285: 2139: 2118: 1387: 1125: 1119: 926: 906: 885: 879: 851: 849: 828: 804: 795: 333:I think it would be a good idea to merge 3159:on its scope), the better it is. Please 4882: 4804:. Equivalently, it is represented by a 4627:States obtained in this way are called 2720:the electron's spin quantum number, and 2630: 2436:Just word that it's for an eigenstate. 2343: 1192:are probabilistic, but the measurement 1078:(The first two sentences, I wrote into 5546:, Diu, and Laloë, F. (1973/1977). And 44:Do not edit the contents of this page. 4798:-valued wave function with values in 4112:, which I find is a redirect page to 3828:; the time-independent wave function 2151:{\displaystyle \{n,\ell ,m_{\ell }\}} 545:is a somewhat theoretical article on 7: 4682:state that is produced is typically 4137:, I find the word 'quantum' absent. 3351:edit is a reversion of another edit. 3295:Knowledge:Revert only when necessary 1196:. (A very minor point of course.) -- 5574:notation, and uses "inner product". 4918:Wavefunction equation does not work 4894:The Principles of Quantum Mechanics 4008:The Principles of Quantum Mechanics 3207:On further checking policy, I find 3135:Checking policy on this, I find at 1510:for position and momentum (at time 1498:<-- This is confusing. What are 1480:), and combinations of these. Here 5488:applies only to euclidean spaces. 5241: 5168: 1522:of the system, we can compute the 1377:of the system, formally denoted as 1273:point for further study. Thanks. 24: 5801:convinced me that you are right. 4668:Foundations of Quantum Mechanics 3290:fair comment in my edit summary. 2723:the proton's spin quantum number. 2109:A question about the lead section 1362:and start the experiment at time 5462:Scalar product vs. inner product 5404: 5393: 5353: 5344: 5327: 5315: 5299: 5288: 5231: 5221: 5180: 5159: 5145: 5099: 5089: 5047: 5030: 5012: 4997: 4957: 4943: 4808:of four variables: one discrete 3039:So what? James Cresser with his 2867:"the above example is pure"? no! 29: 4926:, the wavefunction definition 3265:Adding information to Knowledge 3245:, and mention this change here. 3150:Adding information to Knowledge 5670: 5626:. Shouldn't it be merged with 5409: 5388: 5361: 5340: 5331: 5323: 5293: 5226: 5154: 5094: 5041: 5022: 4962: 4947: 4939: 4120:, I find myself redirected to 3783:Observation and Interpretation 2583: 2567: 2275:all the interested information 1407: 1395: 1343:13:54, 22 September 2011 (UTC) 852: 642:03:06, 18 September 2006 (UTC) 520:03:07, 18 September 2006 (UTC) 1: 4913:13:22, 27 December 2015 (UTC) 4874:15:18, 25 December 2015 (UTC) 4609:the following, in which I am 4066:) 05:19, 9 January 2015 (UTC) 3964:Lectures on Quantum Mechanics 3594:) 02:51, 9 January 2015 (UTC) 3542: 3483:) 07:03, 8 January 2015 (UTC) 3436:==Alternatives to reverting== 3224:"== Tightened the wording of 2952:17:07, 23 December 2013 (UTC) 2827:07:04, 15 November 2012 (UTC) 2811:04:49, 15 November 2012 (UTC) 2781:05:26, 14 November 2012 (UTC) 2041: 1999: 1867: 1808: 1722: 1654: 1549: 1430:<-- right - it seems that 1413:{\displaystyle \sigma =(p,q)} 1329:would work for all, with the 1289:15:58, 12 February 2011 (UTC) 1268:04:58, 1 September 2009 (UTC) 1222:17:29, 21 November 2007 (UTC) 1206:15:40, 21 November 2007 (UTC) 1183:18:46, 20 November 2007 (UTC) 1168:18:28, 20 November 2007 (UTC) 1109:18:19, 20 November 2007 (UTC) 1092:18:01, 20 November 2007 (UTC) 1014:17:08, 17 November 2007 (UTC) 816:{\displaystyle \{\psi _{j}\}} 91:21:59, 13 February 2011 (UTC) 75:"Quantum System" is undefined 5829:11:49, 4 February 2016 (UTC) 5454:12:16, 4 February 2016 (UTC) 4757:17:49, 21 January 2015 (UTC) 4490:15:19, 21 January 2015 (UTC) 4421:03:23, 20 January 2015 (UTC) 4292:Thank you for this response. 4276:21:59, 19 January 2015 (UTC) 4261:21:46, 19 January 2015 (UTC) 4205:18:28, 19 January 2015 (UTC) 4187:01:54, 19 January 2015 (UTC) 4157:08:54, 18 January 2015 (UTC) 4133:or am redirected there from 4076:03:23, 10 January 2015 (UTC) 3946:21:51, 21 January 2015 (UTC) 3723:10:17, 12 January 2015 (UTC) 3533:03:16, 10 January 2015 (UTC) 3108:00:07, 25 January 2014 (UTC) 2937:10:04, 6 December 2013 (UTC) 2861:00:10, 22 January 2013 (UTC) 2761:19:22, 7 November 2012 (UTC) 2742:07:08, 3 November 2012 (UTC) 2714:the azimuthal quantum number 2446:23:28, 2 November 2012 (UTC) 2432:22:46, 2 November 2012 (UTC) 2398:15:44, 2 November 2012 (UTC) 2382:18:01, 1 November 2012 (UTC) 2240:14:33, 1 November 2012 (UTC) 2226:04:50, 1 November 2012 (UTC) 2207:14:40, 31 October 2012 (UTC) 2187:13:22, 31 October 2012 (UTC) 2168:06:17, 31 October 2012 (UTC) 2095:11:58, 27 January 2012 (UTC) 2065:20:20, 26 January 2012 (UTC) 2023:22:18, 25 January 2012 (UTC) 1985:10:33, 25 January 2012 (UTC) 1962:15:13, 24 January 2012 (UTC) 1940:11:33, 24 January 2012 (UTC) 1920:01:16, 24 January 2012 (UTC) 1891:00:41, 24 January 2012 (UTC) 1860:16:07, 22 January 2012 (UTC) 1832:00:25, 22 January 2012 (UTC) 1785:23:18, 21 January 2012 (UTC) 1746:22:21, 21 January 2012 (UTC) 1705:22:10, 21 January 2012 (UTC) 1678:21:39, 21 January 2012 (UTC) 1633:18:43, 21 January 2012 (UTC) 1573:17:20, 21 January 2012 (UTC) 1518:"However, knowing the state 996:02:25, 28 October 2007 (UTC) 953:09:21, 25 October 2007 (UTC) 779:00:28, 25 October 2007 (UTC) 768:21:40, 24 October 2007 (UTC) 731:05:47, 25 October 2007 (UTC) 708:. Comments are appreciated. 672:19:41, 5 February 2007 (UTC) 607:05:31, 10 January 2011 (UTC) 117:00:53, 20 January 2011 (UTC) 5808:11:42, 4 January 2016 (UTC) 5788:09:39, 4 January 2016 (UTC) 5772:06:15, 4 January 2016 (UTC) 5747:Measurement interpretations 5731:22:11, 2 January 2016 (UTC) 5697:21:41, 2 January 2016 (UTC) 5652:19:05, 2 January 2016 (UTC) 5637:18:52, 2 January 2016 (UTC) 5610:17:41, 2 January 2016 (UTC) 5550:(1968). And Zettili (2009). 5495:14:24, 2 January 2016 (UTC) 5268:14:57, 3 January 2016 (UTC) 4762:Ballentine (1998) pp. 47–48 3990:09:07, 9 January 2015 (UTC) 3871:03:32, 9 January 2015 (UTC) 3802:15:19, 9 January 2015 (UTC) 3679:11:30, 9 January 2015 (UTC) 3604:11:35, 9 January 2015 (UTC) 3511:20:07, 9 January 2015 (UTC) 3493:07:06, 8 January 2015 (UTC) 3364:==Unacceptable reversions== 3285:01:38, 8 January 2015 (UTC) 3253:02:20, 31 August 2014 (UTC) 3198:00:42, 8 January 2015 (UTC) 3131:00:02, 8 January 2015 (UTC) 3061:22:11, 9 January 2014 (UTC) 3035:16:33, 9 January 2014 (UTC) 3017:21:42, 7 January 2014 (UTC) 2995:18:43, 7 January 2014 (UTC) 2980:11:58, 7 January 2014 (UTC) 2913:14:28, 21 August 2013 (UTC) 2897:09:03, 20 August 2013 (UTC) 2882:12:57, 19 August 2013 (UTC) 2717:the magnetic quantum number 2638:Zettili, Nouredine (2009). 2351:Zettili, Nouredine (2009). 1536:<-- Now this returns to 5872: 5857:15:25, 29 March 2016 (UTC) 4780:05:37, 22 April 2015 (UTC) 4637:When performing a certain 3305:"==Acceptable reversions== 2662:Ballentine, L. E. (1970), 1653:which has been done now.-- 823:with say an integer index 750:01:23, 11 April 2008 (UTC) 686:23:40, 10 March 2007 (UTC) 324:12:00, 30 April 2007 (UTC) 298:23:18, 23 March 2006 (UTC) 4468:refers to the state of a 4093:refers to the state of a 2680:10.1103/RevModPhys.42.358 2668:Reviews of Modern Physics 2522:, where the state vector 2468:refers to the state of a 2261:refers to the state of a 1348:"Clarification needed"... 1333:parameter unnecessary. ᛭ 1309:20:03, 16 June 2011 (UTC) 894:{\displaystyle \psi _{j}} 614: 281:22:34, 13 July 2009 (UTC) 148:11:44, 2 April 2007 (UTC) 5275:Yes, certainly. One has 4643:probability distribution 3818:, it is said to be in a 3137:Knowledge:Editing policy 2789:Minor formatting problem 2697:)06:23, 3 November 2012 1327:particle number operator 1064:probability distribution 843:. Physicists just write 665:experimental predictions 627:21:24, 9 June 2006 (UTC) 496:19:08, 2 June 2006 (UTC) 467:02:27, 23 May 2006 (UTC) 434:15:50, 22 May 2006 (UTC) 401:06:00, 22 May 2006 (UTC) 388:02:45, 22 May 2006 (UTC) 350:02:35, 22 May 2006 (UTC) 220:02:28, 22 May 2006 (UTC) 199:tautologous? I've seen 175:23:22, 12 May 2007 (UTC) 4828:11:48, 1 May 2015 (UTC) 4806:complex-valued function 4592:00:07, 2 May 2015 (UTC) 4565:14:54, 1 May 2015 (UTC) 2472:. It's specified by a 2265:. It's specified by a 1602:future observations of 1247:05:05, 9 May 2009 (UTC) 720:15:41, 6 May 2007 (UTC) 696:Conceptual introduction 355:I might support making 5684: 5426: 5368: 5251: 5201: 5116: 5070: 4976: 2602: 2508: 2332: 2152: 1588: 1414: 1323:basis (linear algebra) 1135: 1073: 988: 972: 935: 915: 895: 867: 865:{\displaystyle |j: --> 837: 817: 677:new first paragraph - 5685: 5534:(1961). Also, mostly 5427: 5369: 5252: 5202: 5117: 5071: 4977: 4680:(v. 1), pp. 6–7.: --> 3980:agreement with Dirac. 3079:Statistical vs. mixed 2603: 2509: 2507:{\displaystyle \{n\}} 2333: 2153: 1584: 1415: 1136: 1134:{\displaystyle L^{2}} 1047: 978: 962: 936: 916: 896: 868: 838: 818: 650:Background info added 165:comment was added by 154:Uncertainty principle 42:of past discussions. 5660: 5384: 5281: 5214: 5134: 5082: 4992: 4933: 3273:edit that was undone 2526: 2492: 2284: 2117: 1386: 1118: 925: 905: 878: 848: 827: 794: 758:Inaccuracy in intro? 486:Please DO NOT merge 5799:Quantum measurement 4709:configuration space 4135:Physical phenomenon 3922:of the system."< 3852:Mécanique Quantique 3045:continuous spectrum 577:, especially since 5680: 5422: 5364: 5247: 5197: 5112: 5066: 4972: 3902:with normalizable 2970:has eigenvectors. 2598: 2504: 2328: 2195:the reference desk 2148: 1952:Sounds good to me. 1410: 1131: 959:statements such as 931: 911: 891: 862: 833: 813: 712:one would expect. 555:molecular orbitals 18:Talk:Quantum state 5754: 5538:, Fortunato, and 5469: 5210:which means that 4449:quantum mechanics 4114:Quantum mechanics 3971:978-1-107-02872-2 3928:Quantum Mechanics 3848:Quantum Mechanics 3642:, the next state 3186:WP:Citing sources 3170:original research 3098:comment added by 3092:be statistical. 3005:position operator 2851:comment added by 2619:Erwin Schrödinger 2553: 2552: 2040:leave it out". -- 1455:"At a later time 1426:prepare the state 1279:comment added by 1250: 1233:comment added by 934:{\displaystyle j} 914:{\displaystyle j} 836:{\displaystyle j} 595:Talk:Energy level 553:article to cover 547:Quantum mechanics 178: 107:comment added by 72: 71: 54: 53: 48:current talk page 5863: 5806: 5770: 5761:(In response to 5760: 5752: 5695: 5689: 5687: 5686: 5681: 5673: 5635: 5587:(1932/1955) and 5573: 5504:Bra–ket notation 5493: 5476:(In response to 5475: 5467: 5439: 5431: 5429: 5428: 5423: 5412: 5407: 5396: 5391: 5373: 5371: 5370: 5365: 5360: 5359: 5347: 5330: 5322: 5321: 5306: 5305: 5296: 5291: 5266: 5256: 5254: 5253: 5248: 5234: 5229: 5224: 5206: 5204: 5203: 5198: 5187: 5183: 5177: 5176: 5171: 5162: 5157: 5152: 5148: 5122:(normalization). 5121: 5119: 5118: 5113: 5102: 5097: 5092: 5076:(orthogonality), 5075: 5073: 5072: 5067: 5056: 5055: 5050: 5044: 5039: 5038: 5033: 5021: 5020: 5015: 5006: 5005: 5000: 4981: 4979: 4978: 4973: 4965: 4960: 4946: 4903:Silly old Dirac. 4897: 4887: 4671: 4631:, as opposed to 3973:, page xvi.: --> 3920:stationary state 3917: 3907: 3901: 3841: 3833: 3827: 3822:state of energy 3817: 3650: 3641: 3628: 3621: 3616:"A knowledge of 3174:reliable sources 3168:and must not be 3110: 3042: 2863: 2683: 2682: 2659: 2653: 2652: 2635: 2607: 2605: 2604: 2599: 2597: 2596: 2590: 2586: 2574: 2570: 2561: 2560: 2554: 2548: 2544: 2539: 2513: 2511: 2510: 2505: 2366: 2365: 2348: 2337: 2335: 2334: 2329: 2324: 2323: 2311: 2310: 2157: 2155: 2154: 2149: 2144: 2143: 2063: 2021: 1889: 1830: 1744: 1676: 1651:wikiproject page 1571: 1434:is position and 1419: 1417: 1416: 1411: 1291: 1249: 1227: 1140: 1138: 1137: 1132: 1130: 1129: 1054:, as opposed to 940: 938: 937: 932: 920: 918: 917: 912: 900: 898: 897: 892: 890: 889: 873: 870: 869: 863: 855: 842: 840: 839: 834: 822: 820: 819: 814: 809: 808: 615:Keep'em seperate 456:stationary state 419:stationary state 377:stationary state 357:stationary state 160: 119: 63: 56: 55: 33: 32: 26: 5871: 5870: 5866: 5865: 5864: 5862: 5861: 5860: 5837: 5817:User:Petr Matas 5802: 5766: 5751: 5749: 5691: 5658: 5657: 5631: 5560: 5544:Cohen-Tannoudji 5489: 5480:) I think that 5466: 5464: 5437: 5382: 5381: 5352: 5314: 5298: 5279: 5278: 5262: 5212: 5211: 5178: 5166: 5143: 5132: 5131: 5080: 5079: 5045: 5028: 5010: 4995: 4990: 4989: 4931: 4930: 4920: 4901: 4900: 4888: 4884: 4835: 4789:After my edit: 4787: 4764: 4738:: 172–198.: --> 4722:: 109–139.: --> 4713:Schrödinger, E. 4669: 4599: 4462:quantum physics 4122:Physical system 4110:Quantum physics 4087:quantum physics 4083: 3997: 3953: 3926:, (1937/1956). 3909: 3903: 3884: 3878: 3835: 3829: 3823: 3815: 3809: 3759: 3730: 3706:: 312–319.: --> 3686: 3669:eigenfunctions. 3662:: 354–357.: --> 3649: 3643: 3640: 3634: 3624: 3617: 3611: 3545: 3182:inline citation 3116: 3093: 3081: 3040: 2960: 2921: 2869: 2846: 2838: 2797:pure state and 2791: 2687: 2686: 2661: 2660: 2656: 2649: 2637: 2636: 2632: 2615:Albert Einstein 2582: 2578: 2566: 2562: 2529: 2524: 2523: 2518:formulation of 2490: 2489: 2462:quantum physics 2370: 2369: 2362: 2350: 2349: 2345: 2315: 2302: 2282: 2281: 2279:quantum numbers 2276: 2255:quantum physics 2135: 2115: 2114: 2111: 1472:, its momentum 1424:We say that we 1384: 1383: 1350: 1316: 1297: 1274: 1256: 1228: 1150:quantum physics 1121: 1116: 1115: 1082:.) Comments? -- 923: 922: 903: 902: 881: 876: 875: 845: 844: 825: 824: 800: 792: 791: 760: 706:State (physics) 698: 661: 652: 617: 331: 288: 184: 161:—The preceding 156: 125: 102: 98: 83:201.215.210.189 77: 59: 30: 22: 21: 20: 12: 11: 5: 5869: 5867: 5836: 5833: 5832: 5831: 5813: 5812: 5811: 5810: 5791: 5790: 5763:diff/698132139 5748: 5745: 5744: 5743: 5742: 5741: 5740: 5739: 5738: 5737: 5736: 5735: 5734: 5733: 5708: 5707: 5706: 5705: 5704: 5703: 5702: 5701: 5700: 5699: 5679: 5676: 5672: 5668: 5665: 5628:scalar product 5615: 5614: 5613: 5612: 5595: 5594: 5593: 5592: 5578: 5577: 5576: 5575: 5554: 5553: 5552: 5551: 5522: 5521: 5520: 5519: 5486:scalar product 5478:diff/697869911 5463: 5460: 5459: 5458: 5457: 5456: 5434: 5433: 5432: 5421: 5418: 5415: 5411: 5406: 5402: 5399: 5395: 5390: 5376: 5375: 5374: 5363: 5358: 5355: 5350: 5346: 5342: 5339: 5336: 5333: 5329: 5325: 5320: 5317: 5312: 5309: 5304: 5301: 5295: 5290: 5286: 5246: 5243: 5240: 5237: 5233: 5228: 5223: 5219: 5208: 5207: 5196: 5193: 5190: 5186: 5182: 5175: 5170: 5165: 5161: 5156: 5151: 5147: 5142: 5139: 5124: 5123: 5111: 5108: 5105: 5101: 5096: 5091: 5087: 5077: 5065: 5062: 5059: 5054: 5049: 5043: 5037: 5032: 5027: 5024: 5019: 5014: 5009: 5004: 4999: 4983: 4982: 4971: 4968: 4964: 4959: 4955: 4952: 4949: 4945: 4941: 4938: 4919: 4916: 4899: 4898: 4881: 4880: 4834: 4831: 4815: 4814: 4810:quantum number 4786: 4783: 4763: 4760: 4745: 4744: 4743: 4742: 4741: 4740: 4729:Heisenberg, W. 4700: 4699: 4698: 4697: 4696: 4695: 4656: 4655: 4654: 4653: 4652: 4651: 4598: 4595: 4576: 4575: 4574: 4573: 4572: 4571: 4570: 4569: 4568: 4567: 4543: 4542: 4541: 4540: 4539: 4538: 4537: 4536: 4535: 4534: 4521: 4520: 4519: 4518: 4517: 4516: 4515: 4514: 4513: 4512: 4499: 4498: 4497: 4496: 4495: 4494: 4493: 4492: 4470:quantum system 4451:describes the 4430: 4429: 4428: 4427: 4426: 4425: 4424: 4423: 4402: 4401: 4400: 4399: 4398: 4397: 4396: 4395: 4383:Léon Rosenfeld 4372: 4371: 4370: 4369: 4368: 4367: 4366: 4365: 4354: 4353: 4352: 4351: 4350: 4349: 4348: 4347: 4336: 4335: 4334: 4333: 4332: 4331: 4330: 4329: 4318: 4317: 4316: 4315: 4314: 4313: 4312: 4311: 4300: 4299: 4298: 4297: 4296: 4295: 4294: 4293: 4283: 4282: 4281: 4280: 4279: 4278: 4245: 4244: 4243: 4242: 4236: 4235: 4234: 4233: 4227: 4226: 4225: 4224: 4218: 4217: 4216: 4215: 4208: 4207: 4118:Quantum system 4095:quantum system 4082: 4079: 4047: 4046: 4045: 4044: 4043: 4042: 4031: 4030: 4029: 4028: 4027: 4026: 4014: 4013: 4012: 4011: 3996: 3993: 3977: 3976: 3975: 3974: 3952: 3949: 3934: 3933: 3932: 3931: 3877: 3874: 3858: 3857: 3856: 3855: 3808: 3805: 3789: 3788: 3787: 3786: 3758: 3755: 3750: 3749: 3748: 3747: 3737:Heisenberg, W. 3729: 3726: 3710: 3709: 3708: 3707: 3685: 3682: 3666: 3665: 3664: 3663: 3647: 3638: 3610: 3607: 3573: 3572: 3571: 3570: 3569: 3568: 3567: 3566: 3565: 3564: 3544: 3541: 3540: 3539: 3538: 3537: 3536: 3535: 3516: 3515: 3514: 3513: 3473: 3472: 3471: 3470: 3469: 3468: 3460: 3459: 3458: 3457: 3456: 3455: 3446: 3445: 3444: 3443: 3442: 3441: 3437: 3429: 3428: 3427: 3426: 3425: 3424: 3423:of his crimes. 3415: 3414: 3413: 3412: 3411: 3410: 3401: 3400: 3399: 3398: 3397: 3396: 3387: 3386: 3385: 3384: 3383: 3382: 3373: 3372: 3371: 3370: 3369: 3368: 3365: 3357: 3356: 3355: 3354: 3353: 3352: 3343: 3342: 3341: 3340: 3339: 3338: 3329: 3328: 3327: 3326: 3325: 3324: 3315: 3314: 3313: 3312: 3311: 3310: 3306: 3261: 3260: 3259: 3258: 3257: 3256: 3234: 3233: 3232: 3231: 3230: 3229: 3205: 3204: 3203: 3202: 3201: 3200: 3153: 3115: 3112: 3080: 3077: 3076: 3075: 3074: 3073: 3072: 3071: 3070: 3069: 3068: 3067: 2968:point spectrum 2959: 2956: 2955: 2954: 2925:Wave functions 2920: 2917: 2916: 2915: 2905:145.107.68.226 2900: 2899: 2868: 2865: 2853:129.118.41.225 2837: 2834: 2832: 2830: 2829: 2790: 2787: 2786: 2785: 2784: 2783: 2766: 2765: 2764: 2763: 2745: 2744: 2726: 2725: 2724: 2721: 2718: 2715: 2712: 2710:quantum number 2708:the principal 2685: 2684: 2654: 2647: 2629: 2628: 2627: 2626: 2610: 2609: 2595: 2589: 2585: 2581: 2577: 2573: 2569: 2565: 2559: 2551: 2547: 2542: 2538: 2535: 2532: 2520:EPR experiment 2503: 2500: 2497: 2470:quantum system 2453: 2452: 2451: 2450: 2449: 2448: 2416: 2415: 2414: 2413: 2401: 2400: 2368: 2367: 2360: 2342: 2341: 2340: 2339: 2327: 2322: 2318: 2314: 2309: 2305: 2301: 2298: 2295: 2292: 2289: 2274: 2263:quantum system 2247: 2246: 2245: 2244: 2243: 2242: 2210: 2209: 2190: 2189: 2147: 2142: 2138: 2134: 2131: 2128: 2125: 2122: 2110: 2107: 2106: 2105: 2104: 2103: 2102: 2101: 2100: 2099: 2098: 2097: 2074: 2073: 2072: 2071: 2070: 2069: 2068: 2067: 2030: 2029: 2028: 2027: 2026: 2025: 1990: 1989: 1988: 1987: 1969: 1968: 1967: 1966: 1965: 1964: 1945: 1944: 1943: 1942: 1925: 1924: 1923: 1922: 1904: 1903: 1902: 1901: 1894: 1893: 1843: 1842: 1841: 1840: 1839: 1838: 1837: 1836: 1835: 1834: 1796: 1795: 1794: 1793: 1792: 1791: 1790: 1789: 1788: 1787: 1773: 1770: 1755: 1754: 1753: 1752: 1751: 1750: 1749: 1748: 1712: 1711: 1710: 1709: 1708: 1707: 1683: 1682: 1681: 1680: 1636: 1635: 1620: 1619: 1594: 1593: 1583: 1582: 1579: 1546: 1545: 1515: 1421: 1420: 1409: 1406: 1403: 1400: 1397: 1394: 1391: 1380: 1379: 1349: 1346: 1315: 1312: 1296: 1295:Quantum system 1293: 1255: 1252: 1209: 1208: 1171: 1170: 1155: 1154: 1153: 1143: 1142: 1128: 1124: 1097: 1096: 1095: 1094: 1046: 1045: 1044: 1043: 1042: 1041: 1033: 1032: 1031: 1030: 1029: 1028: 1019: 1018: 1017: 1016: 999: 998: 987: 986: 985: 984: 977: 976: 971: 970: 969: 968: 961: 960: 956: 955: 946: 930: 910: 888: 884: 861: 858: 854: 832: 812: 807: 803: 799: 787: 782: 781: 759: 756: 755: 754: 753: 752: 734: 733: 697: 694: 683:220.101.73.119 676: 660: 657: 651: 648: 647: 646: 645: 644: 616: 613: 612: 611: 610: 609: 527: 526: 525: 524: 523: 522: 503: 502: 501: 500: 499: 498: 478: 476: 475: 474: 473: 472: 471: 470: 469: 441: 440: 439: 438: 437: 436: 406: 405: 404: 403: 391: 390: 330: 327: 317: 316: 302: 287: 284: 266: 265: 264: 263: 262: 261: 260: 259: 258: 257: 244: 243: 242: 241: 240: 239: 238: 237: 227: 226: 225: 224: 223: 222: 208: 207: 206: 205: 201:billiard balls 183: 180: 155: 152: 151: 150: 124: 121: 97: 96:Unintelligible 94: 76: 73: 70: 69: 64: 52: 51: 34: 23: 15: 14: 13: 10: 9: 6: 4: 3: 2: 5868: 5859: 5858: 5854: 5850: 5846: 5842: 5834: 5830: 5826: 5822: 5818: 5815: 5814: 5809: 5805: 5800: 5795: 5794: 5793: 5792: 5789: 5785: 5781: 5776: 5775: 5774: 5773: 5769: 5764: 5758: 5746: 5732: 5728: 5724: 5720: 5719: 5718: 5717: 5716: 5715: 5714: 5713: 5712: 5711: 5710: 5709: 5698: 5694: 5674: 5666: 5655: 5654: 5653: 5649: 5645: 5640: 5639: 5638: 5634: 5629: 5625: 5624:inner product 5621: 5620: 5619: 5618: 5617: 5616: 5611: 5607: 5603: 5599: 5598: 5597: 5596: 5590: 5586: 5582: 5581: 5580: 5579: 5571: 5567: 5563: 5558: 5557: 5556: 5555: 5549: 5545: 5541: 5537: 5533: 5529: 5526: 5525: 5524: 5523: 5517: 5513: 5509: 5505: 5501: 5500: 5499: 5498: 5497: 5496: 5492: 5487: 5483: 5482:inner product 5479: 5473: 5461: 5455: 5451: 5447: 5443: 5442:wave function 5435: 5419: 5416: 5413: 5380: 5379: 5377: 5356: 5348: 5337: 5334: 5318: 5310: 5302: 5277: 5276: 5274: 5273: 5272: 5271: 5270: 5269: 5265: 5260: 5244: 5238: 5194: 5191: 5188: 5184: 5173: 5149: 5137: 5129: 5128: 5127: 5109: 5106: 5078: 5063: 5060: 5052: 5035: 5017: 5007: 5002: 4988: 4987: 4986: 4966: 4950: 4936: 4929: 4928: 4927: 4925: 4917: 4915: 4914: 4910: 4906: 4895: 4891: 4890:Dirac, P.A.M. 4886: 4883: 4879: 4876: 4875: 4871: 4867: 4862: 4860: 4859:Hilbert space 4856: 4850: 4848: 4847:Hilbert space 4844: 4839: 4830: 4829: 4825: 4821: 4813: 4811: 4807: 4803: 4802: 4797: 4792: 4791: 4790: 4784: 4782: 4781: 4777: 4773: 4769: 4761: 4759: 4758: 4754: 4750: 4737: 4734: 4730: 4726: 4721: 4718: 4714: 4710: 4706: 4705: 4704: 4703: 4702: 4701: 4693: 4692:wave function 4689: 4685: 4679: 4678:0-387-11683-4 4676: 4672: 4665: 4664: 4663: 4662: 4661: 4660: 4659: 4648: 4644: 4640: 4636: 4634: 4630: 4624: 4620: 4619: 4618: 4617: 4616: 4615: 4614: 4612: 4608: 4604: 4596: 4594: 4593: 4589: 4585: 4580: 4566: 4562: 4558: 4553: 4552: 4551: 4550: 4549: 4548: 4547: 4546: 4545: 4544: 4531: 4530: 4529: 4528: 4527: 4526: 4525: 4524: 4523: 4522: 4509: 4508: 4507: 4506: 4505: 4504: 4503: 4502: 4501: 4500: 4491: 4487: 4483: 4479: 4476:, called the 4475: 4474:Hilbert space 4471: 4467: 4466:quantum state 4463: 4459: 4458:Quantum state 4454: 4453:quantum state 4450: 4446: 4445:wave function 4442: 4441:Wave function 4438: 4437: 4436: 4435: 4434: 4433: 4432: 4431: 4422: 4418: 4414: 4410: 4409: 4408: 4407: 4406: 4405: 4404: 4403: 4392: 4388: 4387:Rosenfeld, L. 4384: 4381:According to 4380: 4379: 4378: 4377: 4376: 4375: 4374: 4373: 4362: 4361: 4360: 4359: 4358: 4357: 4356: 4355: 4344: 4343: 4342: 4341: 4340: 4339: 4338: 4337: 4326: 4325: 4324: 4323: 4322: 4321: 4320: 4319: 4308: 4307: 4306: 4305: 4304: 4303: 4302: 4301: 4291: 4290: 4289: 4288: 4287: 4286: 4285: 4284: 4277: 4273: 4269: 4264: 4263: 4262: 4258: 4254: 4249: 4248: 4247: 4246: 4240: 4239: 4238: 4237: 4231: 4230: 4229: 4228: 4222: 4221: 4220: 4219: 4212: 4211: 4210: 4209: 4206: 4202: 4198: 4194: 4191: 4190: 4189: 4188: 4184: 4180: 4174: 4171: 4167: 4163: 4159: 4158: 4154: 4150: 4145: 4143: 4142:Quantum state 4138: 4136: 4132: 4127: 4123: 4119: 4115: 4111: 4106: 4104: 4101:, called the 4100: 4099:Hilbert space 4096: 4092: 4091:quantum state 4088: 4080: 4078: 4077: 4073: 4069: 4065: 4061: 4055: 4051: 4040: 4039: 4038: 4037: 4036: 4035: 4034: 4024: 4023: 4022: 4021: 4020: 4019: 4018: 4009: 4005: 4004:Dirac, P.A.M. 4001: 4000: 3999: 3998: 3994: 3992: 3991: 3987: 3983: 3972: 3969: 3965: 3961: 3957: 3956: 3955: 3954: 3950: 3948: 3947: 3943: 3939: 3929: 3925: 3921: 3916: 3912: 3906: 3899: 3895: 3891: 3887: 3882: 3881: 3880: 3879: 3875: 3873: 3872: 3868: 3864: 3853: 3849: 3845: 3839: 3832: 3826: 3821: 3813: 3812: 3811: 3810: 3806: 3804: 3803: 3799: 3795: 3784: 3780: 3779:Rosenfeld, L. 3775: 3771: 3767: 3763: 3762: 3761: 3760: 3756: 3754: 3746: 3744: 3738: 3734: 3733: 3732: 3731: 3727: 3725: 3724: 3720: 3716: 3705: 3702: 3698: 3694: 3690: 3689: 3688: 3687: 3683: 3681: 3680: 3676: 3672: 3661: 3658: 3654: 3646: 3637: 3632: 3631:Eigenfunktion 3627: 3620: 3615: 3614: 3613: 3612: 3608: 3606: 3605: 3601: 3597: 3593: 3589: 3584: 3580: 3576: 3562: 3561: 3560: 3559: 3558: 3557: 3556: 3555: 3554: 3553: 3552: 3550: 3534: 3530: 3526: 3522: 3521: 3520: 3519: 3518: 3517: 3512: 3508: 3504: 3499: 3498: 3497: 3496: 3495: 3494: 3490: 3486: 3482: 3478: 3466: 3465: 3464: 3463: 3462: 3461: 3452: 3451: 3450: 3449: 3448: 3447: 3438: 3435: 3434: 3433: 3432: 3431: 3430: 3421: 3420: 3419: 3418: 3417: 3416: 3407: 3406: 3405: 3404: 3403: 3402: 3393: 3392: 3391: 3390: 3389: 3388: 3379: 3378: 3377: 3376: 3375: 3374: 3366: 3363: 3362: 3361: 3360: 3359: 3358: 3349: 3348: 3347: 3346: 3345: 3344: 3335: 3334: 3333: 3332: 3331: 3330: 3321: 3320: 3319: 3318: 3317: 3316: 3307: 3304: 3303: 3302: 3301: 3300: 3299: 3298: 3296: 3291: 3287: 3286: 3282: 3278: 3274: 3269: 3266: 3254: 3251: 3247: 3244: 3240: 3239: 3238: 3237: 3236: 3235: 3227: 3223: 3222: 3221: 3220: 3219: 3218: 3217: 3215: 3210: 3199: 3195: 3191: 3187: 3183: 3179: 3175: 3171: 3167: 3162: 3158: 3154: 3152: 3151: 3146: 3145: 3144: 3143: 3142: 3141: 3140: 3138: 3133: 3132: 3128: 3124: 3120: 3113: 3111: 3109: 3105: 3101: 3100:12.104.156.25 3097: 3091: 3087: 3078: 3064: 3063: 3062: 3058: 3054: 3050: 3046: 3038: 3037: 3036: 3032: 3028: 3024: 3020: 3019: 3018: 3014: 3010: 3006: 3002: 2998: 2997: 2996: 2992: 2988: 2984: 2983: 2982: 2981: 2977: 2973: 2969: 2965: 2957: 2953: 2949: 2945: 2941: 2940: 2939: 2938: 2934: 2930: 2926: 2918: 2914: 2910: 2906: 2902: 2901: 2898: 2894: 2890: 2886: 2885: 2884: 2883: 2879: 2875: 2874:145.107.69.79 2866: 2864: 2862: 2858: 2854: 2850: 2842: 2835: 2833: 2828: 2824: 2820: 2815: 2814: 2813: 2812: 2808: 2804: 2800: 2796: 2788: 2782: 2778: 2774: 2770: 2769: 2768: 2767: 2762: 2758: 2754: 2749: 2748: 2747: 2746: 2743: 2739: 2735: 2731: 2727: 2722: 2719: 2716: 2713: 2711: 2707: 2706: 2704: 2700: 2699: 2698: 2696: 2692: 2681: 2677: 2673: 2669: 2665: 2658: 2655: 2650: 2648:9780470026786 2645: 2641: 2634: 2631: 2624: 2620: 2616: 2612: 2611: 2587: 2579: 2575: 2571: 2563: 2549: 2545: 2540: 2536: 2533: 2530: 2521: 2517: 2498: 2487: 2486:hydrogen atom 2483: 2479: 2478:Hilbert space 2475: 2471: 2467: 2466:quantum state 2463: 2459: 2458: 2457: 2447: 2443: 2439: 2435: 2434: 2433: 2429: 2425: 2420: 2419: 2418: 2417: 2410: 2405: 2404: 2403: 2402: 2399: 2395: 2391: 2386: 2385: 2384: 2383: 2379: 2375: 2363: 2361:9780470026786 2358: 2354: 2347: 2344: 2320: 2316: 2312: 2307: 2303: 2299: 2296: 2293: 2290: 2280: 2272: 2271:Hilbert space 2268: 2264: 2260: 2259:quantum state 2256: 2252: 2251: 2250: 2241: 2237: 2233: 2229: 2228: 2227: 2223: 2219: 2214: 2213: 2212: 2211: 2208: 2204: 2200: 2196: 2192: 2191: 2188: 2184: 2180: 2176: 2172: 2171: 2170: 2169: 2165: 2161: 2140: 2136: 2132: 2129: 2126: 2123: 2108: 2096: 2092: 2088: 2084: 2083: 2082: 2081: 2080: 2079: 2078: 2077: 2076: 2075: 2066: 2061: 2060: 2056: 2052: 2047: 2045: 2038: 2037: 2036: 2035: 2034: 2033: 2032: 2031: 2024: 2019: 2018: 2014: 2010: 2005: 2003: 1996: 1995: 1994: 1993: 1992: 1991: 1986: 1982: 1978: 1973: 1972: 1971: 1970: 1963: 1959: 1955: 1951: 1950: 1949: 1948: 1947: 1946: 1941: 1937: 1933: 1929: 1928: 1927: 1926: 1921: 1917: 1913: 1908: 1907: 1906: 1905: 1898: 1897: 1896: 1895: 1892: 1887: 1886: 1882: 1878: 1873: 1871: 1864: 1863: 1862: 1861: 1857: 1853: 1849: 1833: 1828: 1827: 1823: 1819: 1814: 1812: 1806: 1805: 1804: 1803: 1802: 1801: 1800: 1799: 1798: 1797: 1786: 1782: 1778: 1774: 1771: 1769: 1765: 1764: 1763: 1762: 1761: 1760: 1759: 1758: 1757: 1756: 1747: 1742: 1741: 1737: 1733: 1728: 1726: 1720: 1719: 1718: 1717: 1716: 1715: 1714: 1713: 1706: 1702: 1698: 1693: 1689: 1688: 1687: 1686: 1685: 1684: 1679: 1674: 1673: 1669: 1665: 1660: 1658: 1652: 1648: 1644: 1640: 1639: 1638: 1637: 1634: 1630: 1626: 1622: 1621: 1617: 1613: 1609: 1605: 1601: 1596: 1595: 1590: 1589: 1587: 1580: 1577: 1576: 1575: 1574: 1569: 1568: 1564: 1560: 1555: 1553: 1543: 1539: 1535: 1533: 1529: 1523: 1521: 1516: 1513: 1509: 1505: 1501: 1497: 1495: 1491: 1487: 1483: 1479: 1475: 1471: 1467: 1463: 1458: 1453: 1452: 1451: 1449: 1445: 1441: 1437: 1433: 1429: 1425: 1404: 1401: 1398: 1392: 1389: 1382: 1381: 1378: 1376: 1372: 1369: 1365: 1361: 1357: 1352: 1351: 1347: 1345: 1344: 1340: 1336: 1332: 1328: 1324: 1320: 1313: 1311: 1310: 1306: 1302: 1294: 1292: 1290: 1286: 1282: 1278: 1270: 1269: 1265: 1261: 1253: 1251: 1248: 1244: 1240: 1236: 1232: 1224: 1223: 1219: 1215: 1207: 1203: 1199: 1198:B. Wolterding 1195: 1191: 1187: 1186: 1185: 1184: 1180: 1176: 1169: 1165: 1161: 1160:B. Wolterding 1156: 1151: 1147: 1146: 1145: 1144: 1126: 1122: 1113: 1112: 1111: 1110: 1106: 1102: 1093: 1089: 1085: 1081: 1077: 1076: 1075: 1074: 1072: 1069: 1065: 1061: 1057: 1053: 1039: 1038: 1037: 1036: 1035: 1034: 1025: 1024: 1023: 1022: 1021: 1020: 1015: 1011: 1007: 1006:B. Wolterding 1003: 1002: 1001: 1000: 997: 994: 990: 989: 982: 981: 980: 979: 974: 973: 966: 965: 964: 963: 958: 957: 954: 951: 950:B. Wolterding 947: 944: 928: 908: 886: 882: 859: 856: 830: 805: 801: 788: 784: 783: 780: 777: 772: 771: 770: 769: 766: 757: 751: 747: 743: 738: 737: 736: 735: 732: 729: 724: 723: 722: 721: 718: 717:B. Wolterding 713: 709: 707: 702: 695: 693: 689: 687: 684: 678: 674: 673: 670: 666: 658: 656: 649: 643: 640: 636: 635:oppose merger 633: 632: 631: 630: 629: 628: 625: 624:65.211.131.10 621: 608: 604: 600: 596: 592: 588: 587:Excited state 584: 580: 576: 572: 571:Excited state 568: 564: 560: 559:Quantum state 556: 552: 548: 544: 543:Quantum state 540: 536: 535:Quantum state 532: 531:Oppose merger 529: 528: 521: 518: 514: 513:oppose merger 511: 510: 509: 508: 507: 506: 505: 504: 497: 494: 489: 485: 484: 483: 482: 481: 480: 479: 468: 465: 461: 460:quantum state 457: 453: 449: 448: 447: 446: 445: 444: 443: 442: 435: 432: 428: 424: 423:excited state 420: 416: 412: 411: 410: 409: 408: 407: 402: 399: 395: 394: 393: 392: 389: 386: 382: 378: 374: 373:quantum state 370: 366: 365:excited state 362: 358: 354: 353: 352: 351: 348: 344: 343:excited state 340: 339:excited state 336: 328: 326: 325: 322: 321:B. Wolterding 314: 310: 305: 304: 303: 300: 299: 296: 292: 285: 283: 282: 278: 274: 270: 254: 253: 252: 251: 250: 249: 248: 247: 246: 245: 235: 234: 233: 232: 231: 230: 229: 228: 221: 218: 214: 213: 212: 211: 210: 209: 202: 198: 195: 194: 193: 192: 191: 188: 181: 179: 176: 172: 168: 167:138.251.252.7 164: 153: 149: 146: 141: 140: 139: 135: 131: 128: 123:Too technical 122: 120: 118: 114: 110: 106: 95: 93: 92: 88: 84: 80: 74: 68: 65: 62: 58: 57: 49: 45: 41: 40: 35: 28: 27: 19: 5838: 5750: 5569: 5565: 5561: 5503: 5465: 5209: 5125: 4984: 4921: 4902: 4893: 4885: 4877: 4863: 4851: 4843:state vector 4842: 4840: 4836: 4820:178.38.123.1 4816: 4800: 4793: 4788: 4765: 4746: 4735: 4732: 4719: 4716: 4687: 4683: 4667: 4657: 4632: 4629:mixed states 4628: 4626: 4622: 4610: 4600: 4581: 4577: 4557:178.38.123.1 4478:state vector 4477: 4465: 4444: 4390: 4175: 4172: 4168: 4164: 4160: 4146: 4139: 4107: 4103:state vector 4102: 4090: 4084: 4056: 4052: 4048: 4032: 4015: 4007: 3978: 3963: 3960:Weinberg, S. 3935: 3927: 3919: 3914: 3910: 3904: 3897: 3893: 3889: 3885: 3859: 3851: 3847: 3837: 3830: 3824: 3819: 3790: 3782: 3773: 3769: 3765: 3751: 3742: 3741:Zeit. Phys. 3740: 3711: 3703: 3700: 3692: 3667: 3659: 3656: 3644: 3635: 3630: 3625: 3618: 3585: 3581: 3577: 3574: 3546: 3474: 3292: 3288: 3270: 3264: 3262: 3214:this comment 3206: 3149: 3148: 3134: 3117: 3094:— Preceding 3089: 3085: 3082: 3048: 2961: 2922: 2870: 2847:— Preceding 2843: 2839: 2831: 2798: 2794: 2792: 2729: 2702: 2688: 2671: 2667: 2657: 2639: 2633: 2474:state vector 2465: 2454: 2408: 2371: 2352: 2346: 2267:state vector 2258: 2248: 2112: 2058: 2054: 2050: 2043: 2016: 2012: 2008: 2001: 1884: 1880: 1876: 1869: 1847: 1844: 1825: 1821: 1817: 1810: 1739: 1735: 1731: 1724: 1691: 1671: 1667: 1663: 1656: 1646: 1642: 1615: 1611: 1607: 1603: 1599: 1585: 1566: 1562: 1558: 1551: 1547: 1541: 1537: 1531: 1527: 1525: 1519: 1517: 1511: 1507: 1503: 1499: 1493: 1489: 1485: 1481: 1477: 1473: 1469: 1465: 1461: 1456: 1454: 1447: 1443: 1439: 1435: 1431: 1427: 1423: 1422: 1374: 1370: 1363: 1359: 1355: 1353: 1330: 1317: 1298: 1271: 1257: 1225: 1210: 1193: 1190:measurements 1189: 1172: 1098: 1080:this article 1055: 1052:mixed states 1051: 1048: 942: 761: 714: 710: 703: 699: 690: 679: 675: 664: 662: 653: 634: 622: 618: 597:page also. 591:Energy level 583:Ground state 579:Energy level 575:Energy level 567:Ground state 563:Energy level 551:Energy level 539:Energy level 530: 512: 488:energy level 477: 452:ground level 451: 427:ground state 415:energy level 381:energy level 369:ground state 361:energy level 342: 335:Energy level 332: 318: 309:Antiparticle 301: 293: 289: 271: 267: 200: 196: 189: 185: 157: 145:81.156.75.42 136: 132: 129: 126: 109:88.5.175.129 99: 81: 78: 60: 43: 37: 5585:Von Neumann 5444:than here. 5259:Dirac pulse 4725:phase space 4639:measurement 4633:pure states 4603:posted here 4597:a good idea 3924:Kramers, H. 3844:Messiah, A. 3651:, etc."< 3226:WP:CAUTIOUS 3157:limitations 3053:Incnis Mrsi 3009:Incnis Mrsi 2972:Incnis Mrsi 2964:dimensional 2674:: 358–381, 1319:Basis state 1314:Basis state 1281:76.88.4.187 1275:—Preceding 1229:—Preceding 1060:measurement 1056:pure states 874:instead of 599:H Padleckas 464:Fresheneesz 398:Fresheneesz 347:Fresheneesz 313:PCT Theorem 217:Fresheneesz 103:—Preceding 36:This is an 5849:Chjoaygame 5804:Petr Matas 5780:Chjoaygame 5778:existence. 5768:Petr Matas 5757:Chjoaygame 5723:Chjoaygame 5693:Petr Matas 5656:Shouldn't 5644:Chjoaygame 5633:Petr Matas 5602:Chjoaygame 5491:Petr Matas 5472:Chjoaygame 5264:Petr Matas 4905:Chjoaygame 4866:Chjoaygame 4785:Small edit 4772:Chjoaygame 4749:Chjoaygame 4717:Ann. Phys. 4688:pure state 4647:observable 4605:by Editor 4584:Chjoaygame 4482:Chjoaygame 4413:Chjoaygame 4268:W. P. Uzer 4253:Chjoaygame 4214:behaviour. 4193:Chjoaygame 4179:Chjoaygame 4149:Chjoaygame 4131:Phenomenon 4126:Niels Bohr 4068:Chjoaygame 4060:Chjoaygame 3982:Chjoaygame 3938:Chjoaygame 3863:Chjoaygame 3820:stationary 3794:Chjoaygame 3770:attributes 3728:Heisenberg 3715:Chjoaygame 3701:Dialectica 3693:phenomenon 3671:Chjoaygame 3596:Chjoaygame 3588:Chjoaygame 3525:Chjoaygame 3485:Chjoaygame 3477:Chjoaygame 3440:something. 3277:Chjoaygame 3190:Chjoaygame 3166:verifiable 3123:Chjoaygame 2944:Bob K31416 2751:content.-- 2623:Niels Bohr 1468:) at time 1254:Accessible 1068:observable 786:section... 742:RabidDeity 295:scienceman 286:Antimatter 5512:Gottfried 4723:not by a 4650:physics." 3774:relations 3757:Rosenfeld 3250:Kendrick7 3209:this edit 2734:JRSpriggs 2438:IRWolfie- 2232:IRWolfie- 2199:IRWolfie- 2087:IRWolfie- 1977:IRWolfie- 1932:IRWolfie- 1900:progress. 1852:IRWolfie- 1335:LokiClock 901:and call 872:}" /: --> 688:bluehigh 659:Not clear 450:I merged 273:Heimdall2 67:Archive 2 61:Archive 1 5528:Weinberg 4892:(1958). 4733:Z. Phys. 4731:(1927). 4715:(1926). 4439:Over at 4251:morning? 4177:physics. 4006:(1940). 3962:(2013). 3951:Weinberg 3846:(1961). 3697:Bohr, N. 3653:Born, M. 3096:unsigned 3001:in a box 2849:unsigned 2732:states? 2482:electron 1600:given as 1368:momentum 1277:unsigned 1243:contribs 1235:Tunepoet 1231:unsigned 1214:PhySusie 1175:PhySusie 1101:PhySusie 1071:physics. 204:physics. 163:unsigned 105:unsigned 5841:YohanN7 5839:Editor 5821:YohanN7 5755:editor 5536:Auletta 5532:Messiah 5518:(2003). 5470:editor 5446:YohanN7 5257:Like a 4855:vectors 4845:, in a 4611:bolding 4607:Sbyrnes 3876:Kramers 3861:object. 3842:." < 3836:exp (−i 3807:Messiah 3243:WP:BOLD 3178:removed 2889:Mct mht 2819:LaoChen 2773:LaoChen 2753:LaoChen 2730:unbound 2691:LaoChen 2374:LaoChen 2218:LaoChen 2160:LaoChen 1194:results 993:Mct mht 847:}": --> 776:Mct mht 728:Mct mht 593:on the 39:archive 5630:then? 5589:Schiff 5540:Parisi 5436:where 4796:vector 4328:under. 4197:a13ean 3892:exp (− 3766:unique 3657:Nature 3503:a13ean 3337:again. 3323:edits. 3161:boldly 3027:a13ean 2987:a13ean 2929:Nanite 2390:a13ean 2177:is. -- 1581:As for 1508:labels 1488:) and 1260:Ti-30X 1027:etc.". 669:Sangak 639:Anlace 517:Anlace 493:Az7997 425:, and 379:, not 5548:Jauch 5508:Dirac 4857:in a 4711:,< 4684:mixed 4447:, in 3995:Dirac 3816:II.34 2703:bound 2484:in a 2476:of a 2424:Steve 2412:spin. 2269:of a 2179:Steve 1459:: --> 1084:Steve 860:: --> 765:Steve 663:"All 589:into 431:lethe 385:lethe 197:Seems 182:Huh?! 16:< 5853:talk 5845:here 5843:has 5825:talk 5784:talk 5727:talk 5648:talk 5606:talk 5514:and 5450:talk 5261:... 5130:2'. 4909:talk 4870:talk 4824:talk 4776:talk 4768:here 4753:talk 4675:ISBN 4588:talk 4561:talk 4486:talk 4417:talk 4272:talk 4257:talk 4201:talk 4183:talk 4153:talk 4105:. " 4072:talk 4064:talk 3986:talk 3968:ISBN 3942:talk 3867:talk 3838:Et/ħ 3798:talk 3719:talk 3684:Bohr 3675:talk 3609:Born 3600:talk 3592:talk 3549:here 3529:talk 3523:Hmm. 3507:talk 3489:talk 3481:talk 3281:talk 3271:The 3194:talk 3127:talk 3119:Here 3104:talk 3090:must 3086:used 3057:talk 3031:talk 3023:here 3013:talk 2991:talk 2976:talk 2948:talk 2933:talk 2909:talk 2893:talk 2878:talk 2857:talk 2823:talk 2807:talk 2777:talk 2757:talk 2738:talk 2695:talk 2644:ISBN 2621:and 2584:↓ ↑ 2568:↑ ↓ 2516:Bohm 2442:talk 2428:talk 2409:more 2394:talk 2378:talk 2357:ISBN 2236:talk 2222:talk 2203:talk 2183:talk 2175:spin 2164:talk 2091:talk 1981:talk 1958:talk 1936:talk 1916:talk 1856:talk 1781:talk 1766:See 1701:talk 1695:out. 1692:real 1645:and 1629:talk 1614:and 1606:and 1540:and 1530:and 1502:and 1446:and 1339:talk 1305:talk 1285:talk 1264:talk 1239:talk 1218:talk 1202:talk 1179:talk 1164:talk 1105:talk 1088:talk 1010:talk 943:does 746:talk 603:talk 585:and 569:and 561:and 537:and 454:and 429:. - 383:). - 367:and 337:and 311:and 277:talk 171:talk 113:talk 87:talk 5516:Yan 4922:In 4849:." 3894:iEt 3660:119 3309:it. 2803:P0M 2676:doi 2460:In 2253:In 2046:= q 2004:= q 1954:P0M 1912:P0M 1872:= q 1813:= q 1777:P0M 1727:= q 1697:P0M 1659:= q 1625:P0M 1554:= q 1301:P0M 1148:In 975:and 541:. 533:of 5855:) 5827:) 5786:) 5753:To 5729:) 5678:⟩ 5675:ψ 5667:ϕ 5664:⟨ 5650:) 5608:) 5568:, 5506:. 5468:To 5452:) 5401:⟨ 5398:⟩ 5349:− 5338:δ 5308:⟩ 5285:⟨ 5242:∞ 5236:⟩ 5218:⟨ 5164:⟩ 5141:⟨ 5138:∫ 5104:⟩ 5086:⟨ 5058:⟩ 5026:⟨ 5023:⇒ 5008:≠ 4970:⟩ 4967:ψ 4954:⟨ 4951:≡ 4937:ψ 4911:) 4872:) 4826:) 4778:) 4755:) 4736:43 4720:81 4590:) 4563:) 4488:) 4464:, 4419:) 4274:) 4259:) 4203:) 4185:) 4155:) 4089:, 4074:) 3988:) 3944:) 3915:hν 3913:= 3888:= 3869:) 3800:) 3743:43 3721:) 3677:) 3602:) 3531:) 3509:) 3491:) 3297:: 3283:) 3228:== 3196:) 3139:: 3129:) 3106:) 3059:) 3033:) 3015:) 3007:? 2993:) 2978:) 2950:) 2935:) 2911:) 2895:) 2880:) 2859:) 2809:) 2740:) 2672:42 2670:, 2666:, 2576:− 2534:ψ 2464:, 2444:) 2430:) 2396:) 2308:ℓ 2297:ℓ 2257:, 2238:) 2205:) 2197:. 2185:) 2141:ℓ 2130:ℓ 2093:) 2057:× 2053:+ 2015:× 2011:+ 1983:) 1960:) 1938:) 1918:) 1883:× 1879:+ 1858:) 1824:× 1820:+ 1783:) 1738:× 1734:+ 1703:) 1670:× 1666:+ 1631:) 1598:"' 1565:× 1561:+ 1534:." 1450:. 1390:σ 1341:) 1307:) 1287:) 1266:) 1245:) 1241:• 1220:) 1204:) 1181:) 1166:) 1107:) 1090:) 1012:) 883:ψ 802:ψ 748:) 605:) 421:, 363:, 359:, 319:-- 279:) 173:) 115:) 89:) 5851:( 5823:( 5782:( 5759:: 5725:( 5671:| 5646:( 5604:( 5572:) 5570:t 5566:x 5564:( 5562:ψ 5474:: 5448:( 5438:I 5420:, 5417:I 5414:= 5410:| 5405:r 5394:r 5389:| 5362:) 5357:′ 5354:r 5345:r 5341:( 5335:= 5332:) 5328:r 5324:( 5319:′ 5316:r 5311:= 5303:′ 5300:r 5294:| 5289:r 5245:. 5239:= 5232:r 5227:| 5222:r 5195:, 5192:1 5189:= 5185:′ 5181:r 5174:3 5169:d 5160:r 5155:| 5150:′ 5146:r 5110:1 5107:= 5100:r 5095:| 5090:r 5064:0 5061:= 5053:2 5048:r 5042:| 5036:1 5031:r 5018:2 5013:r 5003:1 4998:r 4963:| 4958:r 4948:) 4944:r 4940:( 4907:( 4868:( 4822:( 4801:C 4774:( 4751:( 4670:I 4586:( 4559:( 4484:( 4415:( 4270:( 4255:( 4199:( 4181:( 4151:( 4070:( 4062:( 3984:( 3940:( 3911:E 3905:ψ 3900:) 3898:ħ 3896:/ 3890:φ 3886:ψ 3865:( 3840:) 3831:ψ 3825:E 3796:( 3717:( 3704:2 3673:( 3648:2 3645:ψ 3639:1 3636:ψ 3626:ψ 3619:ψ 3598:( 3590:( 3527:( 3505:( 3487:( 3479:( 3279:( 3255:" 3192:( 3147:" 3125:( 3102:( 3055:( 3041:δ 3029:( 3011:( 2989:( 2974:( 2946:( 2931:( 2907:( 2891:( 2876:( 2855:( 2825:) 2821:( 2805:( 2799:A 2795:A 2779:) 2775:( 2759:) 2755:( 2736:( 2693:( 2678:: 2651:. 2594:) 2588:⟩ 2580:| 2572:⟩ 2564:| 2558:( 2550:2 2546:1 2541:= 2537:⟩ 2531:| 2502:} 2499:n 2496:{ 2440:( 2426:( 2392:( 2380:) 2376:( 2364:. 2326:} 2321:s 2317:m 2313:, 2304:m 2300:, 2294:, 2291:n 2288:{ 2234:( 2224:) 2220:( 2201:( 2181:( 2166:) 2162:( 2146:} 2137:m 2133:, 2127:, 2124:n 2121:{ 2089:( 2062:) 2059:B 2055:v 2051:E 2048:( 2044:F 2020:) 2017:B 2013:v 2009:E 2006:( 2002:F 1979:( 1956:( 1934:( 1914:( 1888:) 1885:B 1881:v 1877:E 1874:( 1870:F 1854:( 1829:) 1826:B 1822:v 1818:E 1815:( 1811:F 1779:( 1743:) 1740:B 1736:v 1732:E 1729:( 1725:F 1699:( 1675:) 1672:B 1668:v 1664:E 1661:( 1657:F 1647:Q 1643:P 1627:( 1618:. 1616:q 1612:p 1608:q 1604:p 1570:) 1567:B 1563:v 1559:E 1556:( 1552:F 1544:. 1542:q 1538:p 1532:q 1528:p 1520:σ 1512:t 1504:Q 1500:P 1494:t 1492:( 1490:Q 1486:t 1484:( 1482:P 1478:t 1476:( 1474:P 1470:t 1466:t 1464:( 1462:Q 1457:t 1448:q 1444:p 1440:σ 1436:p 1432:q 1408:) 1405:q 1402:, 1399:p 1396:( 1393:= 1375:σ 1371:p 1364:t 1360:q 1356:m 1337:( 1331:ν 1303:( 1283:( 1262:( 1237:( 1216:( 1200:( 1177:( 1162:( 1127:2 1123:L 1103:( 1086:( 1008:( 929:j 909:j 887:j 866:} 857:j 853:| 831:j 811:} 806:j 798:{ 744:( 601:( 315:. 275:( 177:. 169:( 111:( 85:( 50:.

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