880:"Total energy" just means kinetic + potential energy. Why don't they just call it energy and be done with it? It's because the motion of bodies is calculated a different way. Normally, we use Newton's law F=ma, and we can say that a body of mass m moved with this trajectory because ot was accelerated by these forces. If we want to calculate the energy total energy = sum of potential and kinetic energies, we can derive it from the speed of the body, and it's movement against the forces. However, you could derive the trajectory of the body a completely different way: use your knowledge of the total energy of the body. If it was a bead moving along a wire, you might know that the total energy is constant. It would be hard to use Newtonian mechanic to calculate what the bead will do. The alternate way of calculating it is called Hamiltonian (classical) mechanics, and the Hamiltonian is just the energy, as I said. But we came at the problem from a different direction, so historically "energy" here has a different name - "hamiltonian".
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can be anywhere in some region of space (i.e., it's not constrained to a discrete set of positions) then your
Hilbert space will be infinite dimensional. Your Hilbert space also depends on how many particles are in your system, how many internal states those particles have, whether they're distinguishable or indistinguishable particles, etc.
1567:, but an even fancier version which I haven't found in TeX yet). See (for example) Shankar's quantum mechanics text book, which uses this convention. I believe I have seen other texts which use this convention as well, and I have certainly had professors use this convention in most of my undergraduate and graduate physics courses.
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the term continues to be used in the same sense. A given operator may have various particular spectrums depending upon boundary conditions. In general fixed boundaries produce descrete spectrums and free boundaries produce continues spectra. (I hope you are still monitoring after the long wait for an answer!) --
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suggests that in the usual schooling one should learn
Hamilton's (classical) mechanics before the quantum mechanical Hamiltonian operator. As well as I remember, I had both courses at the same time, and am not sure in which order I actually learned them, or understood the connection. As is usual in
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By the way, the above point aside, I applaud the clarity of the first sentence "In quantum mechanics, the
Hamiltonian is the operator corresponding to the total energy of the system." One question though: I wonder if the word "corresponding" is less precise than it might be: Are these other bolder
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but I don't think it should be thought of as a quantum mechanics term of art. In functional analysis, the spectrum of an operator is defined by its set of eigenvalues. The spectrum of an operator is sometimes discrete, sometimes continuous and sometimes a combination. Outside of quantum machinics,
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In response to 3, it depends. Say your system consists of one particle with two internal states (say, "spin up" and "spin down") and some finite number n of possible positions. Then the particle has a total of 2n possible states, and your
Hilbert space is 2n dimensional. However, if your particle
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Similarly, I think it's foolish that no where on the page can the equation H*Phi=E*Phi can be found. I know that equation is a huge simplification, but I think I can say with certainty that 80% of the people who come to the page will be most familiar with that equation given that it's frequently the
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I agree, this page does jump into rather technical definitions right away. People don't really need to understand
Hilbert spaces to get an idea of what the Hamiltonian is. The hyperphysics definition is an appropriate one for a 1-dimensional system. In general, it's a measure of the total energy
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If this is unclear, it should probably be clarified somewhere, but I'm not sure if it should be here or in the article on
Hilbert spaces. The latter seems much more focused on the mathematical definition of a Hilbert space... although I think that's probably appropriate. Perhaps we could create a
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Finally, I agree with the previous poster that this page has come down with "properties but not essence" syndrome, wherein the text rambles on about the properties of the subject but not the subject itself. If, as with many things in physics, it's difficult to describe it should be broken down into
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In general, a hat signifies it's a unit vector quantity, a small arrow pointing to the right just above the letter signifies it is a general vector quantity as does a bold symbol. Dots on top signify time derivates and a single quote after the symbol indicates spatial differentiation. If it is not
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Using "the
Hamiltonian" as a noun to refer to the Hamiltonian operator (an operator is a kind of function, so yes they are the same) is a standard shorthand in physics. Another that might trip you up is "Hamiltonian of a system" to mean the value of the Hamiltonian operator for a given system. The
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I've always heard eigenket- not that I've covered bra-ket notation in university yet but I read a lot, and have never come across the word eigenkeit- it's not a word I can find a translation for online either. I'm inclined to say it's a typo, as I think Dirac invented the notation and he certainly
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The problem here isn't that the article isn't clear, simply that people are demanding you be able to read the text without having any knowlage needed to understant what an
Hamiltonian is. Referencing hilbertspaces and dirac notation should be sufficient. The Hamiltonian in the link is one possible
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page, the two are actually the same thing but with different units. That is, it is exactly the same physics. For the most part, we don't have separate articles for the same quantity but in different unit systems. Note, for example, that magnetic field includes both B and H, and we also don't have
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It gives a vector "representing" the total energy? Are you sure? In what way does this vector represent the total energy? As I understand it, the vector that it produces will be the sum of the total energy eigenstate components of the original vector, each multiplied by its corresponding total
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I am not really sure, whether you should give some definition of the hamiltonian without using fundamental concepts like hilbert space and diracs notation. The hyperphysics definiton is just a special case for 1D, 1 Particle etc... for the sake of unversality, one should use the proper notation,
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I came to this page looking for clarification on what my physics text states, however it falls into the exact same esoteric pattern. Exactly what does "total energy of the system" quantify? Further, the next sentence talks about variability in the total energy measured. Thus, in what sense is it
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Also, a lot of people seem to be complaining that the page uses jargon and is inaccessible to laymen. While I agree with these statements entirely (as a neophyte the subject myself), and in other cases I sympathize, I can't imagine how you can make such a sophisticated and complex concept as a
813:{\displaystyle {\hat {H}}=-{\frac {\hbar ^{2}}{2}}\left(\sum _{i}{\frac {1}{m_{i}}}\nabla _{\mathbf {r} _{i}}^{2}+{\frac {1}{2}}\sum _{i\neq j}{\frac {1}{m_{i}+m_{j}}}\nabla _{\mathbf {r} _{i}}\cdot \nabla _{\mathbf {r} _{j}}\right)+V(\mathbf {r} _{1},\ldots ,\mathbf {r} _{N},t)}
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I realize that one often sees the the thing discussed in this article referred to as "The
Hamiltonian", but names like this, in the obvious form of an adjective, cry out the question "Hamiltonian what?". The absence of that being spelled out propagates foggy confusion.
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quantum operator accessible to a non-physicist. I mean, even physicists often struggle to completely understand these things at an intuitive level. This stuff is just plain intrinsically hard. What is the solution to such a problem? Should the page just be deleted?
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Shouldn't there be some sort of link explaining the use of the vertical bar preceding and the arrow following the wave-function phi ? The meaning is not at all clear and therefore the article in its entirety is of little use. Could the author not correct this please ?
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I've not found the information I was looking for (what "Cauchy propagators" are). I think this is the wrong branch of QM; I need one of the time dependent formulations (?) such as
Feynman's. Interesting, though, and worth reviewing before I try to understand that.
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I appreciate that these variants may signify vector, normalized, array and so on, but it's sometimes not clear which meanings apply on this page, why they appear only sometimes, and indeed whether this page uses a particular convention consistently. Thanks.
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While this does not pertain directly to quantum mechanics, Jackson's electrodynamics text uses the script H as a Hamiltonian density (describing the Hamiltonian in terms of continuous fields rather than discrete coordinates), and reserves the typical
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Under what conditions is the latter more appropriate than the former? Where, mathematically, do these terms come from? This needs expansion. My text doesn't mention anything about cross terms. I would be very grateful for clarification!
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I just noticed that the link to "Free States" takes you to a political page about governments and other such nonsense unrelated to the free states of particles in quantum physics. Don't know how to fix it, but there you have
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It is a Hamiltionian function when the Hamiltonian operator has something to operate on. Conveniently, though, you can do the problems without knowing what it is operating on. I suspect that is the reason for the ambiguity.
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terms that will not be understood by the average reader are especially important to define before they are used. I believe this is recursive, and introductory background is often paragraphs in length in similar articles.
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I gather from the article that the full name of the thing under discussion is "Hamiltonian operator", or "Hamiltonian function" (are these the same thing?), and to say so explicitly would be an improvement, I think.
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Much of this article is described with infinite dimensional vectors. That complicates the distinction between discrete and continuum. It might be one of the simplest, yet least obvious, parts of quantum mechanics.
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Is this correct? Incorrect? Close? I have no idea how to read bra-ket notation (and the article on it doesn't help) - so I'm completely lost on this page, as I would guess that *most* people are who've come here.
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Regarding this sentence at the beginning: "It is a Hermitian matrix, that, when multiplied by the column vector representing the state of the system, gives a vector representing the total energy of the system."
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The text says that the spectrum ... is the set...., but the Wiki article for spectrum says that it represents a continuum, whereas, although not linked, the Wiki definition of set refers to "distinct things".
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892:"total energy of the system" isn't jargon, it states the Hamiltonian of a system is the total amount of energy of the system. Besides lacking a definition of energy which is not approriate here.
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I'm no expert, but the first and second sentences of the Introduction seem to me to say practically the same thing, or almost. Surely this badly needs editing. Seems that way to me anyway. AP
955:"Depending on the Hilbert space of the system" How do Hilbert spaces differ? How do they relate to the modeling of physical systems? Are the Hilbert spaces used here of infinite dimensions?
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many courses, the connections to other courses are often assumed, not taught, and often not quite learned. Is it really usual to teach Hamilton's mechanics before the quantum operator?
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I think you mean written using. Written in would refer to the language, but if you mean the structure and syntax, written using such appallingly poor English would be more appropriate.
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introduction to the classical concept before diving straight into operators, in my experience. I have withdrawn that request due to pushback and changes made in the DAB page itself.
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I really don't think the amount of "jargon" this page uses can be substantially further reduced without teaching people quantum mechanics. Should this tag really still be there?
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543:{\displaystyle {\hat {H}}=-{\frac {\hbar ^{2}}{2}}\left(\sum _{i}{\frac {1}{m_{i}}}\nabla _{\mathbf {r} _{i}}^{2}\right)+V(\mathbf {r} _{1},\ldots ,\mathbf {r} _{N},t)}
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Hamiltonian, depending on what forces and interactions you include, the total energy of the given system be defined differently, and thus the Hamiltonian will change.
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The relationship between the Hilbert space containing all possible states of the system (?) and the equation given is not clear. Where is the vector in this space?
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the Hamilton–Jacobi equation is written as a first-order, non-linear partial differential equation for the Hamilton's principal function {\displaystyle S(q,t)}
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There are apparently also Hamiltonian spaces, paths, matrices and so on. Any overview info that would help clarify which of these are related would be welcome!
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The former is the correct one in typical canonical coordinates. Cross terms in the kinetic energy can appear if one e.g. uses relative coordinates (see e.g.
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Re "if you ask me. I think this statement may be someone's misunderstanding.": Yes, that is not correct. The Hamiltonian itself is the energy observable.
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symbol usually represents Hilbert space. Hilbert space is relevant to the Hamiltonian operator, so the symbols should be different to avoid confusion.
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Bra-ket notation has nothing to do with the Hamiltonian specifically, but that link will be for people who haven't come across bra-ket notation yet.
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My guess is that spectrum is referring to some quantum mechanics definition, which is not presently in Knowledge, so probably needs to be
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bold and there is not vector symbol, it should be italic and that represents a magnitude. This is all universal notation.
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This page (like other pages that just jump into bra-ket notation) doesn't explain what the article's subject really is.
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Shouldn't it be eigenkeit instead of eigenket? It's spread around the article and even appears in one of the headings.
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energy. Not much of a "representation", if you ask me. I think this statement may be someone's misunderstanding.
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The above Irish mathematician seems to be ignored throughout Knowledge wherever the term "Hamiltonian" is used. --
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The term spectrum is used in a variety of contexts. Here, the term is probably borrowed from
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first equation presented in Quantum classes having reference to the Hamiltonian operator.
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That raises a fair point, the classes are taken simultaneously. There is, however, always
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The Hamiltonian is the operator, not the system itself, so this change would be incorrect.
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V(r,t): what is r? This should be defined (so should t, although it is probably time).
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has some different advice, which, it says, is particularly important for math articles.
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other ways "Hamiltonian" is used as an ajective are afaik unrelated. Hope this helps.
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It turns out this does have relevance to QM, in the context of quantum field theory.
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maybe with a comment like "If you are not familiar with Dirac-Notation click -: -->
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Why are so many articles in this field written in such appallingly poor English?
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Also, I am not totally sure of this, but I believe "corresponding" refers to the
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Under "Schrodinger formalism", shouldn't the kinetic energy be given as below?
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What is the significance of the following notation variants in this article:
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Eigenket is correct, since it is referring to Dirac bra-ket notation.
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total energy? Is it a probability distribution? An average?
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If these aren't correct, then what does "correspond" mean?
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Agreed. I'll try and clean the introduction up a bit now.
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https://en.wikipedia.org/Hamilton%E2%80%93Jacobi_equation
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since the HJE is first order and non linear.. see this;
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thanks for pointing it out. that link has been removed.
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I've always seen the Hamiltonian written as a straight
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It takes the same form as the Hamilton–Jacobi equation
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I concur. Perhaps some of the words can become links?
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1625:—Preceding
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1130:Fresheneesz
831:24.22.53.72
148:free images
31:not a forum
2288:Categories
2205:Regarding
1183:KristinLee
928:observable
366:DareManWin
1525:Ghazwozza
1450:article.
1422:produces
1360:Eigenket?
1201:WP:JARGON
1006:Mr. Jones
898:WP:JARGON
208:is rated
88:if needed
71:Be polite
21:talk page
2207:g-factor
2124:Gwideman
2084:unsigned
2052:unsigned
1988:Gwideman
1942:Fixed.--
1771:unsigned
1627:unsigned
1618:Notation
1273:unsigned
1222:spectrum
1179:momentum
852:unsigned
346:unsigned
56:get help
29:This is
27:article.
1944:Maschen
1750:Marbini
1735:Marbini
1719:Mct mht
1676:TraceyR
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1366:Sakkura
1351:Mct mht
1258:scanyon
987:Marbini
319:on the
292:Physics
283:Physics
239:Physics
210:C-class
154:WP refs
142:scholar
2016:Xuanji
1569:zipz0p
1468:or as
972:Tim314
935:energy
216:scale.
126:Google
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169:JSTOR
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1992:talk
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1399:talk
1393:. --
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