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An article can usually not give a detailed explanation of all concepts and nomenclatures used to explain its topic. Some basic knowledge of physics and mathematics will generally be required of the reader, to an extent depending on the article's subject. However, where appropriate, links to more
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There are a number of different techniques to produce mathematical formulae on
Knowledge, all with their advantages and disadvantages. Inevitably, this has led to a wide spectrum of preferences among editors and of styles used in articles. Even worse, there is a perpetual change of formatting by
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7315:, and functions required to build formulae) are roughly grouped into three levels of difficulty; school/(advanced) college level, then undergraduate level, finally graduate level (and beyond). Articles which fall into one (or between?) these sections should consider the reader to assume
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It is legitimate to place navboxes in the "see also" or "references" sections if that's where the article ends. Placing navboxes in "see also" sections is beneficial as they display a large collection of related links in one place with minimum wikicode (only template syntax is
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A decision at each article should be made for what kind of template of links to use. Sidebars are a matter of debate for their size and layout of links; some favour their use, others oppose or are neutral. Navboxes are usually less problematic due to their compactness.
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171:. Don't set one formula in a style very different from the rest of the article, and don't do mass changes from one style to another without prior discussion on the talk page. That said, the style recommended for physics articles is as a rule of thumb:
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Of course, other operations not tabulated can be used, provided their use is declared and linked. Most of the operations not tabulated below will be outside the scope of most of physics, such as some non-elementary functions like
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decide what conventions are the easiest for a reader to follow and for internal consistency, and also state clearly (in a section or footnotes?) the prominent alternative conventions used by other authors,
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of links (say, 50 or more) are better as footers than as sidebars, since opening the sections of a sidebar makes it extend a long way down the page, and makes the box and article less readable this way.
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This choice is aiming at a smooth integration of simple inline formulae in the surrounding text, while offering the extended possibilities of LaTeX formatting for more involved displayed formulae.
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Sometimes, reliable and well-established sources use conventions which may lack a clear physical depiction, and WP editors should consider what the best conventions a physics article should have.
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is also employed, but is less common than upright. For consistency throughout articles, please use upright bold. In particular, please do not execute mass changes from bold style to bold-italic.
1135:
3946:. Where possible, please use the "nabla squared" symbol ∇, which appears to be more common in physics, and is more intuitive; ∇ = ∇ ⋅ ∇ is a nicer notation, and less ambiguous for capital delta.
3862:{\displaystyle \nabla ={\frac {\partial }{\partial x}}{\hat {\mathbf {e} }}_{x}+{\frac {\partial }{\partial y}}{\hat {\mathbf {e} }}_{y}+{\frac {\partial }{\partial z}}{\hat {\mathbf {e} }}_{z}}
3631:{\displaystyle \nabla ={\hat {\mathbf {e} }}_{x}{\frac {\partial }{\partial x}}+{\hat {\mathbf {e} }}_{y}{\frac {\partial }{\partial y}}+{\hat {\mathbf {e} }}_{z}{\frac {\partial }{\partial z}}}
3120:) should be italicized. A specific script used as a tensor index may give a hint about nature of the corresponding linear space – this distinction should be used whenever possible. For example,
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and similarly for any other coordinates. It is clear this way that the derivatives are operators not acting on the basis vectors (which can have spatial dependence in a local coordinate frame).
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2016:
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appear to be universal, although their exact definitions can depend on the subject. Unless an article deals explicitly with these fundamental concepts, it should not explain the meaning of
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unless the present Manual specifies otherwise. Notations that are popular in a certain context should be used; unusual or otherwise less common notation (for physics) should be avoided.
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1639:{\displaystyle R({\hat {n}},\phi )\equiv e^{-{\frac {i}{\hbar }}\phi \,\mathbf {J} \cdot {\hat {\mathbf {n} }}}\,,\quad e^{{\frac {i}{\hbar }}(\mathbf {p} \cdot \mathbf {x} -Et)}}
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environment always typesets lower case Greek letters in italic, and upper case ones in roman type. For consistency within an article, Greek letters produced using HTML or
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for the sake of compact mathematical statements - they simply create more work in explaining and linking the notations, while contributing no understanding to the
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only adds more whitespace. Both can be avoided by having the image floating in the top-right corner and the sidebar below, or replacing the sidebar with a navbox.
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for an example of this case. Representation of units and numerical quantities (where a numerical value and a unit are specified explicitly) should comply with
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are usually assumed by most people. When using other unit systems which are extensively employed in practice although may be unfamiliar to laymen, including:
1485:{\displaystyle R({\hat {n}},\phi )\equiv e^{-i\phi \,\mathbf {J} \cdot {\hat {\mathbf {n} }}/\hbar }\,,\quad e^{i(\mathbf {p} \cdot \mathbf {x} -Et)/\hbar }}
771:
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it should be explicitly stated they are going to be used before using them. There are several sets of natural units, each with their own applications, so
436:. If they are used, the same symbol should be used for the same quantity consistently throughout the article. (There is also a variant for the lowercase
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An image directly corresponding to the specific topic of an article should have priority for putting in the top right corner over a sidebar template.
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Physics is such an enormous subject that an article should specify the relevant branch(es) of it, unless the concept is physically universal. Known
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243:. Paying attention to this seemingly minor detail helps to immediately make clear the meaning of a particular notation, and should not be seen as
1329:{\displaystyle R({\hat {n}},\phi )\equiv \exp \left(-{\frac {i}{\hbar }}\phi \,\mathbf {J} \cdot {\hat {\mathbf {n} }}\right)\,,\quad \exp \left}
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to have enough explanation to make clear the relevance of the mathematics to physics (for instance, why a simpler formulation is not possible?),
6630:
6700:(QFT, implies QM, SR, background in classical field theory) – not necessary to mention if one of well-known derived theories is used directly:
5633:{\displaystyle \displaystyle P=P_{0}+9807{\frac {\mathrm {Pa} }{\mathrm {m} }}h\displaystyle 2\rho _{\mathrm {Al} }<\rho _{\mathrm {Fe} }}
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may be compact, but is pointless since the notation has to be explained (constituting no thermodynamics). The law can be stated in words:
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The brackets are often dropped by sources since it is known the integral symbol always includes the differentials (in the above example "
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as well as physics-related parts of other articles. For consistency with the rest of
Knowledge, other manuals of style (in particular
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4058:, to parallel the Laplacian ∇. The notation without the square is already known to denote the D'Alembertian. Either can be used (?)
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707:, it should be denoted as a constant (in italics). In particular, the elementary charge, even when treated as a unit, is denoted
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3031:
1908:
765:(upright). For dimensions, an exception occurs when denoting the dimension of an arbitrary quantity is necessary, as in ""; see
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So these are not exactly the same, differentials are more general. Following are the recommended applications of the notation.
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9083:. prepared under the direction of the AIP Publication Board (4th ed.). New York, N.Y.: American Institute of Physics. 1990.
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Generally, the first is used in simpler contexts, while index notation is used to make advanced manipulations simpler. The
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One of the most basic, though often ignored typesetting conventions for mathematical formulae concerns the use of upright (
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for chemistry) apply when possible. Exceptions and additional conventions specific to physics topics are described here.
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for an example) to reflect specific choices made and prevent other editors performing mass-changes to other conventions.
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The following everyday units are presumed to be known and needn't be explained, although ideally linked at least once.
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of an operator using the same letter as for the operator itself, the operator should have a hat to distinguish the two.
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235:(including abbreviations, names of particles, chemical elements and units of measurement) should be set in roman type.
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Placing an image in the center, while placing a template in the corner, creates large amounts of whitespace, and the
5312:. Use templates, wiki code formatting, and HTML tags to match the main text, both for inline and displayed formulae.
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Note that in the last example, "ext" is a text label (an abbreviation for "external") and is thus set roman, while
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in MeV when the reader thinks of kg (or decimal prefixes thereof) is confusing, a related point is that writing "
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however using the forward slash for division as above is acceptable, although extra brackets are usually needed,
723:). These symbols are also never prefixed with SI prefixes. Related units that are denoted in roman type include
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Aside from units, there are cases where specific choices of mathematical entities have to be made, notably the
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topics, where it's hard to find an image that's clearly associated with the article, (e.g. articles related to
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must be clear. Ideally, natural units shouldn't be used, due to lack of familiarity and potential confusion by
5956:{\displaystyle \mathrm {SU} (n),\mathrm {SO} (n),\mathrm {SL} (2,\mathbb {C} ),\mathrm {U} (n),\mathrm {O} (n)}
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templates may be used to generate HTML/Unicode equivalents for the \langle and \rangle glyphs of <math: -->
8750:, etc., will not be easily understood to the typical reader, and obviously never expected. Such topics need
4785:"). Nevertheless: for the sake of clarity an extra pair of brackets will not clutter, and should be included.
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if references (databooks, handbooks, appendices of books etc.) present measurements in terms of those units.
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operators for
Minkowski space may lead to confusion, especially so in indefinite-metric spaces even between
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Lower case Greek letters that denote names of particles, and that don't appear in the same article within a
1728:: easy to hand-write and indicates clearly a quantity with direction, although it becomes messy with other
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as the full entity with no reference to specific components (which uses the boldface notations above), or
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for a good example), at the very top to provide an immediate visual depiction of what the article says.
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2503:, then the use of different styles for tensor fields of different types would be confusing too, even in
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1806:: is often used for position vectors for example the position vector from point A to B would be written
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995:{\displaystyle i\hbar {\frac {d}{dt}}\left|\Psi \right\rangle ={\hat {H}}\left|\Psi \right\rangle \,.}
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5846:\mathrm{SU}(n), \mathrm{SO}(n), \mathrm{SL}(2,\mathbb{C}), \mathrm{U}(n), \mathrm{O}(n)</math: -->
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In vector expressions for the gradient ∇, with respect to a given basis, the basis vectors should be
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should thus follow the same convention. This practice applies to both normal and bold font weight.
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Exponential functions are very common in physics, representing growth and decay from solutions of
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to a typical reader, since the symbols have to be explained by editors and/or read up by readers.
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International vocabulary of metrology – Basic and general concepts and associated terms (VIM)
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is a variable and is this set in italic. This type of notation is sometimes used instead of
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is extensively used throughout physics and mathematics. Due to technical limitations, the
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For partial derivatives this is not a problem, since differentials are never written as "
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The capital delta symbol is universally reserved for changes in quantities, for example Δ
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Formulae of (nuclear or particle) reactions should not be formatted with <math: -->
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is a general way to determine infinitesimal changes of a quantity using a derivative.
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The main principles to be considered when deciding about a particular formatting are
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Often, an article is well-served with a picture, diagram, or even an animation (see
3374:. Distinction of indices is especially helpful when one tensor quantity is built on
2909:, such as non-italicized Greek letters. For example, when typesetting the mass of a
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are too long, cluttered, and confusing for non-expert mathematicians: simply write
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Other well-known derived quantities include (and these should ideally be linked):
9060:), the notation with overline is discouraged except for aforementioned two cases.
9044:. Although the complex conjugate of a vector is used in physics (for example, in
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takes those values and the sequence of numbers is infinite. Even though the full
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Template:Editnotices/Page/Mathematical descriptions of the electromagnetic field
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contains guidelines for consistency of style in writing and editing articles on
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are an example (the 4-current is preferred as a 3-form, but sources (including
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Often, integers or half-integers need to be listed (say, listing the number of
3124:-based (four dimensional) objects should be indexed with a subset of lowercase
2352:{\displaystyle {\boldsymbol {A}},\,{\mathsf {A}},\,{\boldsymbol {\mathsf {A}}}}
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Representation of Common mathematical formulae (arithmetic, algebra (including
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clarifies notation for higher derivatives by repeated action of a derivative,
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operator (indexed components), as usual. There are other notations, including
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2250:{\displaystyle {\overrightarrow {\psi }},{\boldsymbol {\psi }},{\hat {\psi }}}
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The dimension of voltage should be written in terms of the base dimensions in
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The lead of an article should specify the one of these, for example (see the
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This proposal has become dormant through lack of discussion by the community.
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to be thoroughly linked to the main subject articles containing the details.
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is a unit and must be denoted as V, a roman capital letter. Brackets mean
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If neither are suitable for any reason, the best resort is to just use the
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and not something else, like a summation dummy variable or tensor indices.
2499:-tensors. Also, if the article has to operate with both vectors and higher
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When a physical constant serves as a unit in some systems, such as in with
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quantities frequently occur, and share the same notation with first order
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HTML: {{bra-ket|''ϕ''|''ψ''}} or {{math| {{bra-ket|''ϕ''| ''ψ''}} }}": -->
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for HTML left/right/doubleheaded arrows over/under one letter, like this:
1668:: easy to typeset and print, and stands out, easily compatible with other
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interest. If you want to revive discussion on this subject, try using the
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247:. The rule has a few notable exceptions, which will be explained below.
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Templates can be used for linking groups of articles, in the form of:
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not require any in-depth explanation (a few words or sentence at most).
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For integrals, either of the notations are employed in the literature:
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are excluded due to its heavy usage as wave functions and fields, and
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WP:Manual of Style/Mathematics § Typesetting of mathematical formulae
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Used only for derivatives, not ratios as above. Advantages include:
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Ideally - not all Greek letters are used for indices. For example,
2845:{\displaystyle \mathbf {B} _{\mathrm {x_{0}} }^{\mathrm {ext} }(t)}
2198:{\displaystyle \left|\psi \right\rangle ,\left\langle \psi \right|}
2074:, rather than bold, arrows, or hats. For the bra-ket notation, the
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boxes of links which are fully collapsible, usually placed at the
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and other domains where index notation is traditionally avoided).
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is a parameter held fixed (though conceptually still a variable).
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Quantities whose values are not given numerically, including both
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9113:"The NIST guide for the use of the International System of Units"
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Symbols for subatomic particles and nuclei can be generated with
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Ratios of differential (infinitesimal) quantities and derivatives
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boxes of links with collapsible sections, usually placed in the
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Generally, all symbols (abbreviations) of units are universally
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Waldron, Anne; Judd, Peggy; Miller, Valerie, eds. (June 2011).
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if the calculation/explanation can easily be done in SI units,
2644:{\displaystyle 2\rho _{\mathrm {Al} }<\rho _{\mathrm {Fe} }}
6754:", etc. so just link to string theory and take it from there?)
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15:
5705:{\displaystyle \displaystyle P=P_{0}+9807{\frac {Pa}{m}}h\,.}
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can be produced using the same syntax as for LaTeX using the
650:, because different typographies apply to them. For example:
464:, which can be useful for the distinction from an upper case
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descriptions of the essential concepts should be provided.
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4236:{\displaystyle \Box ,\partial _{\alpha }\partial ^{\alpha }}
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The same symbol Δ is also used in mathematics to denote the
1943:{\displaystyle {\overrightarrow {A}},{\overrightarrow {AB}}}
1064:. As such they can have quite large/complicated variables.
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be used in some calculations or explanations to illustrate
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exist, and compatibility between them varies. Concepts as
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has to be used, and an intended glyph is not available in
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Subscripts and superscripts follow the general rule about
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4485:{\displaystyle \int _{\partial V}\psi (\mathbf {x} )\,dV}
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2\rho_{\mathrm{Al}} < \rho_{\mathrm{Fe}}</math: -->
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unless the present Manual specifies otherwise. See also:
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6066:{\displaystyle SU(n),SO(n),SL(2,\mathbb {C} ),U(n),O(n)}
4643:{\displaystyle \oint _{\partial D}p(x,y)\,dx+q(x,y)\,dy}
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denoting the boundary of a closed volume is encouraged (
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902:{\displaystyle \mathbf {F} ={\frac {d\mathbf {p} }{dt}}}
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environment, should be set in roman type, following the
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editors who don't like the current style of an article.
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Where chemical notation is used, it should comply with
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whereas fractions using the horizontal stroke are not:
9177:(3rd ed.). International vocabulary of metrology. 2012
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Mathematical descriptions of the electromagnetic field
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Very advanced, abstract, and demanding topics, like;
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Even if the context becomes abstract, statements like
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natural units are better than SI units in the process,
4895:. In cases like this, notations can be misleading, as
4808:, which also frequently occur. For example, the local
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Basic and general concepts and associated terms (VIM)
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Knowledge:Categories, lists, and navigation templates
7883:{\displaystyle \displaystyle \prod \limits _{k}a_{k}}
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of an electrically charged continuum is given by the
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2791:\mathbf{B}_\mathrm{x_0}^\mathrm{ext}(t)</math: -->
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1980:
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1889:
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1694:{\displaystyle {\overrightarrow {\text{overarrows}}}}
1680:
1506:
1350:
1177:
1164:
respectively), the "exp" notation is clearer to read:
1080:
928:
868:
449:
421:
397:
373:
349:
325:
301:
9115:. The National Institute of Standards and Technology
8563:
not always distinguished from matrix multiplication
8055:
The secondary are not essential (just reciprocals):
8007:
The secondary are not essential (just reciprocals):
7831:{\displaystyle \displaystyle \sum \limits _{k}a_{k}}
3928:) throughout - it looks irregular to mix the styles.
3318:
are used; this should be clarified in the context),
3089:
notation is depreciated (with possible exception of
5291:, otherwise they should be typographically similar.
3400:
or upright throughout; mixed styles look irregular.
2882:to indicate that only the functional dependence of
1732:. Underlining is easily possible in HTML using the
7882:
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2010:
1942:
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1130:{\displaystyle e^{i2\pi x/\lambda },e^{i\omega t}}
1129:
994:
901:
455:
427:
403:
379:
355:
331:
307:
8913:) use the 4-current as a 1-form, see the article
8868:to the article; they are likely to contribute to
1987:
1721:{\displaystyle {\underline {\text{underlining}}}}
485:
93:WP:MOSMATH § Typesetting of mathematical formulae
8636:(at least in the simplist forms), including the
8480:
5068:makes clear that differentiation is an operator,
4359:and either is acceptable in WP physics articles.
792:guideline applies to units. For example, write
240:
9128:University of Chicago Press Staff, ed. (2010),
6549:
6459:within context relevant to those main articles,
4072:(very rare), which should be reserved for some
1799:{\displaystyle {\overline {\text{overlining}}}}
8538:
7078:is technically more correct, this is actually
3210:should be indexed with capital Latin letters:
2654:\mathbf{B}_{x_0}^\mathrm{ext}(t)</math: -->
2011:{\displaystyle \mathbf {\hat {e}} ,{\hat {e}}}
1156:For more detailed/complicated arguments, (see
9111:A. Thompson; B. N. Taylor (October 5, 2010).
8892:in SR and GR, and the representations of the
7401:are expected, particular examples including;
7319:familiarity within the scope of the section.
4346:{\displaystyle \int f(x)\,dx,\,\int \,dxf(x)}
8:
7641:{\displaystyle \displaystyle {\frac {a}{b}}}
7322:In all cases, the numbers, operations etc.:
7283:are in thermal equilibruim with each other (
2722:
2583:
2464:
2452:
2430:
2416:
2047:{\displaystyle {\overrightarrow {\hat {e}}}}
486:in a way similar to variables in mathematics
8036:All the primary functions should be known;
6576:, and not natural units for the sake of it.
6541:, is confusing when the reader expects the
4418:"); it is a powerful and compact notation:
2470:{\displaystyle \langle \phi ,\psi \rangle }
2436:{\displaystyle \langle \phi |\psi \rangle }
2344:
2095:mode. There are also specialized templates
58:when complete and universally agreed on by
9026:In pure mathematics, for a complex vector
7526:for scalars, vectors, operators, matrices
6829:requires additional irrelevant explanation
6742:(less known are the specific theories of "
6679:or other intrinsic quantum phenomena like
6590:paradigms, with usual abbreviations, are:
9134:(16th ed.), University of Chicago Press,
8762:Application of graphics and illustrations
7873:
7863:
7856:
7821:
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7804:
7627:
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7390:
7013:which makes it very clear to anyone that
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2781:{\displaystyle 2\rho _{Al}<\rho _{Fe}}
2769:
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2298:, which are reserved for sets (see below
2236:
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1996:
1982:
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9150:Physical Review Style and Notation Guide
8393:
8296:
8185:
8078:
7988:All the primary ratios should be known;
7896:
7473:
6937:without introducing unfamiliar notations
6276:
6179:
5534:
4929:
4761:{\displaystyle \oint _{\partial D}\left}
4083:
2576:
2408:\langle\phi | \psi \rangle</math: -->
789:
282:
8962:
8864:If the contents of a template only has
8773:Knowledge:WikiProject Physics/Templates
7723:complex scalars or 2-component spinors
6552:As a rule of thumb (for natural units):
6523:readers. For example: giving masses of
5696:
4869:{\displaystyle \rho ={\dfrac {dq}{dV}}}
4745:
4716:
4632:
4603:
4474:
4323:
4318:
4307:
4029:. There are other notations, including
3255:Most of other linear spaces, including
2738:2\rho_{Al} < \rho_{Fe}</math: -->
2340:
2328:
2321:
2228:
1891:
1826:{\displaystyle {\overline {\text{AB}}}}
1601:
1584:
1558:
1550:
1477:
1429:
1424:
1395:
1318:
1264:
1235:
1227:
1143:in which case fractions should use the
987:
932:
9095:
8884:Conventions in WP articles and sources
7087:Writing compound statements, like the
6694:(QM, relativistic or non-relativistic)
6452:, ideally should only to be used for:
3026:Index notation for tensors and spinors
2332:
2114:for creating bra and ket vectors, and
1068:For simple arguments on one line, the
8136:(indefinite, definite, and improper)
7326:should be linked to the main articles
7311:The tables below (mainly of numbers,
5739:
4944:Division of infinitesimal quantities
239:This rule explicitly applies also to
7:
6925:greater than and not equal to zero"
6897:", the colon means "such that", and
6723:(application of relativity and QFT):
5786:{\displaystyle \mathbb {N,Q,Z,R,C} }
5746:\mathbb{N, Q, Z, R, C}</math: -->
5315:For all reactions, the arrow symbol
3996:, which should be reserved for some
2299:
2265:usually have a hat, but not always (
657:is a quantity and may be denoted as
7860:
7808:
7215:denote the temperatures of objects
5272:Particles, substances and reactions
4407:a brief explanation such as "where
3984:, which should be reserved for the
2965:{\displaystyle m_{\mathrm {\nu } }}
2396:in a Hilbert space, one should use
917:
8479:possibly by multiple indices; see
7600:means element of any linear space
6539:without referring to natural units
5940:
5923:
5898:
5895:
5878:
5875:
5858:
5855:
5622:
5619:
5604:
5601:
5582:
5577:
5574:
4685:
4577:
4452:
4224:
4214:
3935:for change in position coordinate
3887:
3829:
3825:
3790:
3786:
3751:
3747:
3739:
3619:
3615:
3580:
3576:
3541:
3537:
3508:
3077:), with or without reference to a
2900:An exception can be made when the
2827:
2824:
2821:
2808:
2688:
2685:
2682:
2635:
2632:
2617:
2614:
980:
954:
288:Some Greek letters have a second,
14:
8986:(1977), "The twistor programme",
7670:for scalars, matrices, operators
7095:"The zeroth law can be stated as
6613:, a.k.a. non-relativistic physics
5537:guideline applies to substances:
4515:, frequently the case when (say)
3917:{\displaystyle \bigtriangledown }
2062:vectors, which are elements of a
1898:{\displaystyle {\boldsymbol {A}}}
7385:notation for numbers, including
7170:are the temperatures of objects
5319:should be used, the equals sign
4467:
3843:
3804:
3765:
3597:
3558:
3519:
3407:of the derivative operators. In
2801:
2664:
2294:... (to be decided). Do not use
1984:
1859:
1618:
1610:
1572:
1561:
1456:
1448:
1409:
1398:
1297:
1289:
1249:
1238:
884:
870:
114:The main technical options are:
19:
8988:Reports on Mathematical Physics
8872:, and hence should not be used.
8802:of the article, even after the
7255:is in thermal equilibruim with
7231:is in thermal equilibruim with
6582:Clarifying the relevant physics
5845:
5745:
4899:the derivative is defined as a
4502:for the boundary of the volume.
4162:
4119:
4102:
4089:
2923:, the ν can remain non-italic:
2790:
2737:
2653:
2596:
632:One must carefully distinguish
441:
413:
389:
365:
341:
317:
293:
9042:complex conjugate vector space
6107:{\displaystyle {\mathcal {H}}}
6060:
6054:
6045:
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5882:
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5332:Electron–positron annihilation
4742:
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4713:
4701:
4629:
4617:
4600:
4588:
4471:
4463:
4414:is the boundary of the volume
4340:
4334:
4304:
4298:
3847:
3808:
3769:
3601:
3562:
3523:
3193:Objects constructed of weight-
2839:
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2002:
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1190:
1181:
970:
680:, so = V, and braces {} mean
218:typeface: as a general rule,
1:
7927:for scalar, matrix, operator
7365:, including common constants
3244:{\displaystyle \varphi _{A}.}
3186:standard (Minkowskian) metric
2296:𝕓𝕝𝕒𝕔𝕜𝕓𝕠𝕒𝕣𝕕 𝕓𝕠𝕝𝕕
1961:, they can be bold, or a hat
1589:
1434:
1269:
720:Elementary charge § As a unit
41:or start a discussion at the
9008:10.1016/0034-4877(77)90047-7
8767:Sidebar and navbox templates
7089:zeroth law of thermodynamics
6827:Any abstract notation which
4816:of the infinitesimal charge
4802:differential (infinitesimal)
4796:Notation for differentiation
4498:and removes the need to use
3022:and the latter may be used.
2376:{\displaystyle \mathbb {A} }
1866:{\displaystyle \mathbf {A} }
1818:
1791:
849:Common mathematical formulae
308:{\displaystyle \varepsilon }
9131:The Chicago Manual of Style
7352:always presumed to be known
6436:Old non-SI units (such as "
4879:However, this looks like a
2571:Subscripts and superscripts
241:subscripts and superscripts
9217:
8770:
8584:over complex numbers only,
8265:Including operations with
7919:, make context clear this
7689:including complex numbers
6127:introductory articles and
5479:and as particle reaction:
4919:differential of a function
4793:
4519:in a 2d plane is applied:
4391:For integrations over the
3314:may cause confusion where
404:{\displaystyle \vartheta }
90:
56:WP:Manual of Style/Physics
8946:Help:displaying a formula
7688:
5320:
5316:
4191:{\displaystyle \Box ^{2}}
4051:{\displaystyle \Box ^{2}}
3159:{\displaystyle A^{\mu }.}
2984:looks no different than
1653:Vectors and vector spaces
332:{\displaystyle \epsilon }
294:\varepsilon</math: -->
97:Help:Displaying a formula
67:This part of Knowledge's
8606:Non-elementary functions
6962:condensed matter physics
6837:symbolic logic notations
6764:article) anything like:
5967:
5797:
4939:Usage in the literature
4822:in infinitesimal volume
4513:not enclosed in brackets
3879:When using <math: -->
3118:Van der Waerden notation
3074:Van der Waerden notation
3007:{\displaystyle m_{\nu }}
1749:. There is the template
1035:...) should comply with
729:unified atomic mass unit
356:{\displaystyle \varphi }
8449:only, unless explained
8421:only, unless explained
8245:only, unless explained
8218:only, unless explained
7983:Trigonometric functions
6704:Quantum electrodynamics
3893:{\displaystyle \nabla }
3297:{\displaystyle A_{i},.}
2579:typeface. For example:
1072:notation is legitimate
920:for angular brackets),
518:reduced Planck constant
440:in the Latin alphabet,
428:{\displaystyle \theta }
390:\vartheta</math: -->
175:use wiki markup or the
87:Typesetting of formulae
34:retained for historical
9102:: CS1 maint: others (
8701:Functional integration
8682:Variational derivative
8622:orthogonal polynomials
8298:Multivariable calculus
7915:(Due to conflict with
7892:only finite products?
7884:
7832:
7772:or defined up to sign
7659:Multiplicative inverse
7642:
7433:differential equations
7149:denotes "imples", and
7091:using logic notation:
6873:is a number such that
6710:Quantum chromodynamics
6627:Classical field theory
6579:
6122:Prerequisite knowledge
6108:
6067:
5957:
5822:inline (normal text):
5787:
5734:, not just bold face:
5706:
5634:
4870:
4800:In physics, ratios of
4762:
4644:
4486:
4347:
4237:
4192:
4159:D'Alembertian operator
4139:
4052:
4027:D'Alembertian operator
4019:
3986:D'Alembertian operator
3978:
3918:
3894:
3863:
3632:
3350:
3349:{\displaystyle A^{k}.}
3310:(although the letters
3298:
3245:
3184:is used to denote the
3160:
3008:
2966:
2939:while in <math: -->
2890:is of interest, while
2846:
2782:
2707:
2645:
2471:
2437:
2377:
2353:
2251:
2199:
2048:
2012:
1944:
1899:
1867:
1827:
1800:
1722:
1695:
1640:
1486:
1330:
1131:
1051:differential equations
996:
903:
699:sans-serif type: MLTI.
682:the numerical value of
457:
429:
405:
381:
357:
333:
318:\epsilon</math: -->
309:
9040:is an element of the
8686:fractional derivative
8594:in pure mathematics.
8251:Matrix multiplication
7885:
7833:
7653:may be a scalar only
7643:
7536:(Scalar, of a vector)
7455:is the imaginary unit
6976:dots: ...), like so:
6823:No abstract notations
6677:wave–particle duality
6664:Non-quantum physics:
6631:Newtonian gravitation
6477:(especially wherever
6456:historical relevance,
6109:
6068:
5958:
5844:displayed (\mathrm):
5788:
5707:
5635:
5394:as nuclear reaction:
4871:
4763:
4645:
4511:where integrands are
4487:
4399:, the partial symbol
4348:
4238:
4193:
4140:
4138:{\displaystyle \Box }
4053:
4020:
4018:{\displaystyle \Box }
3979:
3977:{\displaystyle \Box }
3919:
3895:
3864:
3633:
3412:Cartesian coordinates
3378:of different natures.
3376:several linear spaces
3351:
3299:
3246:
3161:
3091:theoretical mechanics
3009:
2967:
2847:
2783:
2708:
2646:
2472:
2438:
2378:
2354:
2286:not in index notation
2252:
2200:
2049:
2013:
1945:
1900:
1868:
1828:
1801:
1723:
1696:
1641:
1487:
1331:
1132:
1057:representations, and
1029:differential geometry
997:
904:
458:
456:{\displaystyle \ell }
430:
406:
382:
380:{\displaystyle \phi }
358:
342:\varphi</math: -->
334:
310:
8705:integration measures
8690:covariant derivative
8032:Hyperbolic functions
7898:Elementary functions
7855:
7803:
7623:
7307:Levels of difficulty
7021:set builder notation
6833:set builder notation
6698:Quantum field theory
6644:Theory of relativity
6621:Analytical mechanics
6525:elementary particles
6094:
5971:
5851:
5751:
5728:standard number sets
5652:
5545:
4835:
4677:
4658:which really means:
4569:
4444:
4289:
4204:
4175:
4129:
4074:covariant derivative
4035:
4009:
3998:covariant derivative
3968:
3908:
3884:
3736:
3505:
3330:
3275:
3225:
3204:spin representations
3140:
2991:
2947:
2796:
2743:
2723:''ext''</sub: -->
2659:
2602:
2449:
2413:
2365:
2317:
2211:
2167:
2124:for inner products.
2024:
1978:
1909:
1887:
1855:
1810:
1783:
1705:
1678:
1504:
1348:
1175:
1162:Schrödinger equation
1078:
926:
914:Schrödinger equation
866:
472:Units and quantities
447:
419:
414:\theta</math: -->
395:
371:
347:
323:
299:
79:for mathematics and
54:Rename this page to
9156:(Revised First ed.)
9000:1977RpMP...12...65P
8931:are necessary (see
8901:Maxwell's equations
8633:Integral transforms
8587:Usually denoted as
8569:Conjugate transpose
8305:Partial derivatives
8279:Undergraduate level
7917:tensor superscripts
7790:Only for integers.
7420:alternating current
7387:scientific notation
7338:, super-roots, and
6852:worded descriptions
6843:quantifier notation
6619:(how well-known is
6617:Newtonian mechanics
6611:Galilean relativity
6294:Common non-SI unit
6197:Common non-SI unit
5744:displayed (LaTeX):
5535:roman versus italic
4904:difference quotient
4395:of a (hyper)volume
3257:3-dimensional space
3030:Two ways to denote
2832:
2693:
2577:roman versus italic
2505:3-dimensional space
858:Newton's second law
790:roman versus italic
767:continuity equation
545:vacuum permittivity
206:Roman versus italic
60:wikiproject physics
31:It is inactive but
9201:Knowledge archives
8981:See, for example,
8905:differential forms
8792:of an article, and
8736:analytic functions
8671:Differential forms
8642:Laplace transforms
8455:Tensor contraction
8348:Multiple integrals
7880:
7879:
7868:
7842:only finite sums?
7828:
7827:
7816:
7638:
7637:
7479:elementary algebra
7350:The following are
6657:General relativity
6651:Special relativity
6280:Physical quantity
6183:Physical quantity
6139:A large number of
6104:
6063:
5953:
5783:
5738:inline (unicode):
5702:
5701:
5697:
5630:
5629:
5628:
5282:Subatomic particle
4866:
4864:
4758:
4746:
4717:
4640:
4633:
4604:
4482:
4475:
4343:
4324:
4319:
4308:
4233:
4188:
4135:
4099:Laplacian operator
4048:
4015:
3974:
3944:Laplacian operator
3914:
3890:
3859:
3628:
3388:If "d" is used in
3346:
3294:
3241:
3156:
3061:in components via
3004:
2962:
2913:ν (nu) in html or
2842:
2799:
2778:
2703:
2662:
2641:
2534:''μ''</sub: -->
2532:''μ''</sup: -->
2513:''μ''</sub: -->
2511:''μ''</sup: -->
2467:
2433:
2373:
2349:
2341:
2329:
2247:
2195:
2070:, the standard in
2044:
2008:
1940:
1895:
1863:
1823:
1796:
1718:
1716:
1691:
1636:
1590:
1585:
1559:
1482:
1435:
1430:
1396:
1326:
1270:
1265:
1236:
1127:
992:
988:
899:
602:electron rest mass
482:physical constants
453:
442:\ell</math: -->
425:
401:
377:
366:\phi</math: -->
353:
329:
305:
292:form, for example
8866:partial relevance
8853:Templates with a
8835:table of contents
8728:exterior calculus
8724:
8723:
8610:special functions
8599:
8598:
8573:Hermitian adjoint
8276:
8275:
7955:Natural logarithm
7921:is exponentiation
7859:
7807:
7710:Complex conjugate
7635:
7426:quantum mechanics
6788:quantum mechanics
6771:quantum mechanics
6744:Heterotic strings
6729:Yang–Mills theory
6692:Quantum mechanics
6604:Classical physics
6432:
6431:
6268:
6267:
6141:physical theories
5966:not recommended:
5796:not recommended:
5730:should be set in
5691:
5586:
5323:is usually wrong.
5289:Nuclide templates
5167:
5166:
4863:
4509:abuse of notation
4246:
4245:
4000:(see next point).
3988:(see next point).
3926:\bigtriangledown
3850:
3836:
3811:
3797:
3772:
3758:
3626:
3604:
3587:
3565:
3548:
3526:
3370:is equivalent to
3112:(see for example
2244:
2222:
2072:quantum mechanics
2066:, should use the
2042:
2037:
2005:
1990:
1938:
1920:
1821:
1817:
1794:
1790:
1775:
1766:
1737:tags, like this:
1712:
1709:
1689:
1685:
1660:Euclidean vectors
1604:
1579:
1553:
1522:
1416:
1366:
1256:
1230:
1193:
973:
948:
916:: displayed (see
897:
575:elementary charge
262:...</math: -->
193:...</math: -->
192:use <math: -->
121:(generated using
106:LaTeX versus HTML
50:
49:
9208:
9186:
9184:
9182:
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9163:
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9120:
9107:
9101:
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9082:
9077:AIP style manual
9061:
9059:
9039:
9037:
9031:
9024:
9018:
9017:
8979:
8973:
8967:
8920:Editors should:
8812:"external links"
8790:top right corner
8656:
8626:Bessel functions
8593:
8581:
8560:
8534:
8518:
8506:
8498:
8488:Bra-ket notation
8476:
8443:
8415:
8403:Exterior product
8387:
8378:
8377:
8340:
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8336:
8335:
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8117:
8115:
8114:
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8106:
8071:
8052:
8023:
8004:
7977:
7964:
7949:must be integer
7948:
7944:
7935:
7930:
7913:
7889:
7887:
7886:
7881:
7878:
7877:
7867:
7840:any linear space
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7494:Additive inverse
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7412:electromagnetism
7377:
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7346:Elementary level
7340:super-logarithms
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7298:
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6998:
6993:
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6988:
6952:, the orders of
6926:
6906:
6900:
6888:
6884:
6846:, others?), are
6813:
6799:and not simply:
6795:
6782:
6721:Particle physics
6670:classical fields
6546:
6536:
6509:particle physics
6481:is applied), and
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4917:calculating the
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4376:integral symbols
4373:
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4090:Not recommended
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4046:
4025:is used for the
4024:
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2584:ext</sub: -->
2563:
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2398:bra-ket notation
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2083:
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2068:bra-ket notation
2054:
2053:
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2030:
2028:
2018:
2017:
2015:
2014:
2009:
2007:
2006:
1998:
1992:
1991:
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1973:
1957:For "normal" or
1950:
1949:
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1186:
1158:angular momentum
1150:
1136:
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1128:
1126:
1125:
1107:
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1102:
1033:complex analysis
1001:
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665:capital letter "
660:
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128:Wiki markup and
23:
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16:
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9209:
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9205:
9191:
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9127:
9118:
9116:
9110:
9094:
9090:
9080:
9074:
9070:
9068:Further reading
9065:
9064:
9045:
9035:
9033:
9027:
9025:
9021:
8982:
8980:
8976:
8968:
8964:
8959:
8942:
8886:
8879:of the article.
8779:
8769:
8764:
8744:operator theory
8651:
8588:
8577:
8553:
8546:Linear operator
8520:
8508:
8500:
8492:
8475:
8465:
8459:
8431:
8407:
8397:linear algebra
8376:
8370:
8369:
8368:
8365:
8326:
8323:
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8281:
8255:
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8101:
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8010:
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7959:
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7852:
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7782:
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7741:
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7699:
7695:Plus-minus sign
7680:
7663:
7650:
7621:
7620:
7610:
7595:
7575:
7565:
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7498:
7448:
7441:
7399:complex numbers
7373:
7367:
7348:
7309:
7296:
7289:
7284:
7272:
7265:
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7248:
7241:
7236:
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7199:
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7154:
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7137:
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7123:
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7109:
7102:
7096:
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7054:
7047:
7043:
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7033:
7032:
7027:
7014:
7000:
6996:
6995:
6990:
6986:
6985:
6980:
6966:quantum numbers
6958:physical optics
6931:since this way
6898:
6886:
6874:
6825:
6820:
6731:(which namely?)
6687:Quantum theory:
6646:(non-Galilean):
6584:
6542:
6528:
6487:(especially in
6173:
6137:
6124:
6115:
6092:
6091:
6080:
5969:
5968:
5849:
5848:
5832:), SL(2, ℂ), U(
5818:, not italic:
5808:
5749:
5748:
5732:blackboard bold
5724:
5719:
5717:Sets and spaces
5680:
5662:
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5649:
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4693:
4680:
4675:
4674:
4671:
4665:
4662:
4572:
4567:
4566:
4532:
4526:
4523:
4517:Green's theorem
4447:
4442:
4441:
4430:
4424:
4421:
4408:
4400:
4385:
4379:
4371:
4365:
4287:
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3553:
3540:
3514:
3503:
3502:
3491:
3488:
3485:
3484:
3482:
3481:
3464:
3461:
3458:
3457:
3455:
3454:
3437:
3434:
3431:
3430:
3428:
3427:
3418:
3396:, it should be
3385:
3367:
3361:
3333:
3328:
3327:
3321:
3316:complex numbers
3311:
3278:
3273:
3272:
3266:
3228:
3223:
3222:
3219:
3213:
3199:
3195:
3194:
3143:
3138:
3137:
3131:
3087:linear operator
3028:
3015:
2994:
2989:
2988:
2977:
2973:
2950:
2945:
2944:
2933:
2927:
2920:
2914:
2896:
2875:
2865:
2863:
2807:
2794:
2793:
2765:
2749:
2741:
2740:
2733:
2725:
2669:
2657:
2656:
2626:
2608:
2600:
2599:
2592:
2586:
2573:
2553:
2545:
2536:
2535:''f'' }} ": -->
2524:
2515:
2514:''f'' }}": -->
2496:
2492:
2447:
2446:
2411:
2410:
2384:
2363:
2362:
2315:
2314:
2306:
2300:sets and spaces
2272:
2266:
2209:
2208:
2184:
2170:
2165:
2164:
2155:
2154:
2145:
2144:
2136:
2128:
2121:
2115:
2111:
2105:
2102:
2096:
2091:
2085:
2081:
2075:
2022:
2021:
1976:
1975:
1969:
1927:
1907:
1906:
1885:
1884:
1876:
1853:
1852:
1846:
1808:
1807:
1781:
1780:
1772:
1763:
1756:
1750:
1733:
1703:
1702:
1676:
1675:
1655:
1591:
1537:
1502:
1501:
1436:
1381:
1346:
1345:
1281:
1277:
1218:
1214:
1173:
1172:
1148:
1145:forward slash /
1111:
1081:
1076:
1075:
1047:
1025:differentiation
976:
950:
940:
924:
923:
889:
879:
864:
863:
851:
830:
806:
782:
776:
754:
743:
732:
714:
708:
658:
623:
619:
616:
614:
611:
605:
592:
589:
586:
584:
578:
566:
562:
559:
557:
554:
548:
536:
532:
529:
527:
521:
508:
505:
503:
497:
488:. Examples are
474:
465:
445:
444:
437:
417:
416:
393:
392:
369:
368:
345:
344:
321:
320:
297:
296:
278:
271:
265:
260:
253:
208:
182:
176:
156:
150:
146:
140:
108:
103:
89:
69:Manual of Style
46:
20:
12:
11:
5:
9214:
9212:
9204:
9203:
9193:
9192:
9188:
9187:
9166:
9144:
9139:
9125:
9108:
9088:
9071:
9069:
9066:
9063:
9062:
9032:its conjugate
9019:
8984:Penrose, Roger
8974:
8961:
8960:
8958:
8955:
8954:
8953:
8948:
8941:
8938:
8937:
8936:
8925:
8894:gamma matrices
8890:metric tensors
8885:
8882:
8881:
8880:
8873:
8870:template creep
8862:
8858:
8851:
8842:Some pages on
8840:
8839:
8838:
8831:
8816:
8815:
8793:
8768:
8765:
8763:
8760:
8759:
8758:
8755:
8748:Hilbert spaces
8722:
8721:
8719:
8717:
8713:
8712:
8710:
8708:
8697:
8696:
8694:
8692:
8678:
8677:
8675:
8673:
8667:
8666:
8663:
8660:
8650:
8649:Graduate level
8647:
8646:
8645:
8629:
8618:error function
8614:gamma function
8612:, namely; the
8601:Additionally:
8597:
8596:
8585:
8582:
8575:
8571:
8565:
8564:
8561:
8551:
8542:
8541:
8535:
8490:
8484:
8483:
8477:
8469:
8463:
8457:
8451:
8450:
8444:
8429:
8427:Tensor product
8423:
8422:
8416:
8405:
8399:
8398:
8391:
8390:
8388:
8372:
8371:
8366:
8363:
8344:
8343:
8341:
8311:
8301:
8300:
8294:
8293:
8290:
8287:
8280:
8277:
8274:
8273:
8263:
8253:
8247:
8246:
8237:
8226:
8220:
8219:
8210:
8199:
8193:
8192:
8190:linear algebra
8183:
8182:
8180:
8161:
8160:
8155:
8140:
8137:
8130:
8129:
8127:
8096:
8093:notation above
8084:
8083:
8076:
8075:
8073:
8034:
8028:
8027:
8025:
7986:
7985:
7979:
7978:
7965:
7957:
7951:
7950:
7937:
7931:
7925:
7907:
7905:Exponentiation
7901:
7900:
7894:
7893:
7890:
7876:
7872:
7866:
7862:
7850:
7844:
7843:
7841:
7838:
7824:
7820:
7814:
7810:
7798:
7792:
7791:
7788:
7780:
7774:
7773:
7771:
7752:
7736:
7725:
7724:
7721:
7712:
7706:
7705:
7697:
7691:
7690:
7687:
7678:
7676:Absolute value
7672:
7671:
7668:
7661:
7655:
7654:
7648:
7634:
7631:
7608:
7602:
7601:
7593:
7573:
7564:
7538:
7534:
7532:Multiplication
7528:
7527:
7524:
7517:
7507:
7496:
7492:
7488:
7482:
7481:
7471:
7470:
7467:
7464:
7437:
7436:
7429:
7423:
7409:
7395:
7394:
7380:
7347:
7344:
7331:
7330:
7327:
7308:
7305:
7304:
7303:
7302:
7301:
7294:
7287:
7270:
7263:
7246:
7239:
7211:
7204:
7197:
7187:
7186:
7185:
7184:
7166:
7159:
7152:
7135:
7128:
7121:
7114:
7107:
7100:
7084:
7083:
7076:
7075:
7074:
7067:
7010:
7009:
7008:
7007:
6941:
6940:
6929:
6928:
6927:
6910:
6909:
6908:
6907:
6861:To exemplify:
6824:
6821:
6819:
6816:
6815:
6814:
6797:
6796:
6783:
6773:, a branch of
6758:
6757:
6756:
6755:
6737:
6735:Standard Model
6732:
6717:
6716:
6715:
6714:
6713:
6707:
6695:
6684:
6662:
6661:
6660:
6654:
6640:
6639:
6638:
6633:and Maxwell's
6624:
6614:
6600:
6583:
6580:
6578:
6577:
6570:
6513:
6512:
6482:
6475:Gaussian units
6464:
6463:
6460:
6457:
6450:imperial units
6434:
6433:
6430:
6429:
6427:
6425:
6423:
6419:
6418:
6416:
6414:
6401:
6395:
6394:
6392:
6390:
6373:
6367:
6366:
6364:
6362:
6341:
6335:
6334:
6332:
6330:
6321:
6315:
6314:
6309:
6307:
6302:
6296:
6295:
6292:
6286:
6281:
6270:
6269:
6266:
6265:
6263:
6257:
6251:
6245:
6244:
6234:
6232:
6226:
6220:
6219:
6217:
6211:
6205:
6199:
6198:
6195:
6189:
6184:
6172:
6171:Expected units
6169:
6136:
6133:
6123:
6120:
6119:
6118:
6101:
6084:Hilbert spaces
6079:
6076:
6075:
6074:
6062:
6059:
6056:
6053:
6050:
6047:
6044:
6041:
6038:
6035:
6032:
6028:
6024:
6021:
6018:
6015:
6012:
6009:
6006:
6003:
6000:
5997:
5994:
5991:
5988:
5985:
5982:
5979:
5976:
5964:
5952:
5949:
5946:
5942:
5938:
5935:
5932:
5929:
5925:
5921:
5918:
5914:
5910:
5907:
5904:
5900:
5897:
5893:
5890:
5887:
5884:
5880:
5877:
5873:
5870:
5867:
5864:
5860:
5857:
5842:
5807:
5804:
5803:
5802:
5794:
5781:
5778:
5775:
5772:
5769:
5766:
5763:
5760:
5757:
5742:
5726:Where needed,
5723:
5720:
5718:
5715:
5714:
5713:
5700:
5695:
5690:
5686:
5683:
5677:
5674:
5669:
5665:
5661:
5658:
5642:
5641:
5624:
5621:
5616:
5612:
5606:
5603:
5598:
5594:
5590:
5584:
5579:
5576:
5570:
5567:
5562:
5558:
5554:
5551:
5531:
5530:
5529:
5528:
5522:
5521:
5512:
5511:
5502:
5501:
5494:
5493:
5476:
5475:
5474:
5473:
5467:
5466:
5457:
5456:
5447:
5446:
5439:
5438:
5429:
5428:
5420:
5419:
5410:
5409:
5401:
5400:
5389:
5383:
5382:
5375:
5374:
5365:
5364:
5357:
5356:
5347:
5346:
5339:
5338:
5325:
5324:
5313:
5299:
5292:
5273:
5270:
5266:
5265:
5169:
5168:
5165:
5164:
5163:
5162:
5161:
5160:
5069:
5063:
5037:
5012:Derivative of
5009:
5008:
5001:
4956:
4941:
4940:
4937:
4934:
4923:
4922:
4915:
4912:linear algebra
4906:, but also an
4877:
4876:
4861:
4858:
4853:
4850:
4843:
4840:
4810:charge density
4791:
4788:
4787:
4786:
4771:
4770:
4769:
4756:
4752:
4749:
4744:
4741:
4738:
4735:
4732:
4729:
4726:
4723:
4720:
4715:
4712:
4709:
4706:
4703:
4700:
4696:
4690:
4687:
4683:
4666:
4663:
4655:
4654:
4653:
4652:
4639:
4636:
4631:
4628:
4625:
4622:
4619:
4616:
4613:
4610:
4607:
4602:
4599:
4596:
4593:
4590:
4587:
4582:
4579:
4575:
4527:
4524:
4504:
4503:
4500:another symbol
4495:
4494:
4493:
4492:
4481:
4478:
4473:
4469:
4465:
4462:
4457:
4454:
4450:
4425:
4422:
4389:
4361:
4360:
4356:
4355:
4354:
4353:
4342:
4339:
4336:
4333:
4330:
4327:
4322:
4317:
4314:
4311:
4306:
4303:
4300:
4297:
4294:
4270:
4255:
4248:
4247:
4244:
4243:
4230:
4226:
4220:
4216:
4212:
4209:
4199:
4185:
4181:
4161:
4155:
4154:
4150:
4146:
4134:
4118:
4112:
4111:
4106:
4101:
4095:
4094:
4091:
4088:
4080:
4079:
4078:
4077:
4059:
4045:
4041:
4014:
4003:
4002:
4001:
3989:
3973:
3953:
3947:
3940:
3929:
3913:
3889:
3876:
3875:
3872:
3871:
3870:
3856:
3849:
3845:
3834:
3831:
3827:
3822:
3817:
3810:
3806:
3795:
3792:
3788:
3783:
3778:
3771:
3767:
3756:
3753:
3749:
3744:
3741:
3726:
3699:
3672:
3642:
3641:
3640:
3639:
3624:
3621:
3617:
3610:
3603:
3599:
3591:
3585:
3582:
3578:
3571:
3564:
3560:
3552:
3546:
3543:
3539:
3532:
3525:
3521:
3513:
3510:
3477:
3450:
3423:
3401:
3384:
3381:
3380:
3379:
3358:
3357:
3356:
3345:
3340:
3336:
3307:
3306:
3305:
3304:
3293:
3290:
3285:
3281:
3253:
3252:
3251:
3240:
3235:
3231:
3215:
3190:
3189:
3169:
3168:
3167:
3166:
3155:
3150:
3146:
3114:Ricci calculus
3083:
3082:
3068:Ricci calculus
3063:index notation
3059:
3027:
3024:
3020:
3019:
3001:
2997:
2982:
2981:
2958:
2953:
2937:
2936:
2931:
2894:
2873:
2861:
2855:
2854:
2841:
2838:
2835:
2829:
2826:
2823:
2814:
2810:
2803:
2775:
2772:
2768:
2764:
2759:
2756:
2752:
2748:
2729:
2716:
2715:
2702:
2699:
2696:
2690:
2687:
2684:
2676:
2672:
2666:
2637:
2634:
2629:
2625:
2619:
2616:
2611:
2607:
2590:
2572:
2569:
2568:
2567:
2566:
2565:
2541:
2520:
2481:
2480:
2479:
2466:
2463:
2460:
2457:
2454:
2432:
2429:
2425:
2421:
2418:
2402:Hermitian form
2390:
2389:
2388:
2371:
2346:
2339:
2334:
2327:
2323:
2282:
2260:
2259:
2258:
2243:
2240:
2234:
2230:
2226:
2221:
2218:
2193:
2190:
2187:
2183:
2179:
2176:
2173:
2057:
2056:
2055:
2041:
2036:
2033:
2004:
2001:
1995:
1989:
1986:
1955:
1954:
1953:
1952:
1951:
1937:
1933:
1930:
1924:
1919:
1916:
1893:
1861:
1834:
1820:
1793:
1778:
1715:
1688:
1673:
1654:
1651:
1650:
1649:
1648:
1647:
1633:
1630:
1627:
1624:
1620:
1616:
1612:
1608:
1603:
1600:
1594:
1588:
1578:
1574:
1567:
1563:
1557:
1552:
1549:
1544:
1540:
1536:
1533:
1530:
1527:
1521:
1518:
1512:
1509:
1495:
1494:
1493:
1479:
1475:
1471:
1468:
1465:
1462:
1458:
1454:
1450:
1446:
1443:
1439:
1433:
1426:
1422:
1415:
1411:
1404:
1400:
1394:
1391:
1388:
1384:
1380:
1377:
1374:
1371:
1365:
1362:
1356:
1353:
1339:
1338:
1337:
1324:
1320:
1316:
1312:
1309:
1306:
1303:
1299:
1295:
1291:
1287:
1284:
1280:
1276:
1273:
1268:
1262:
1255:
1251:
1244:
1240:
1234:
1229:
1226:
1221:
1217:
1213:
1210:
1207:
1204:
1201:
1198:
1192:
1189:
1183:
1180:
1166:
1165:
1153:
1152:
1140:
1139:
1138:
1137:
1124:
1121:
1118:
1114:
1110:
1105:
1101:
1097:
1094:
1091:
1088:
1084:
1055:complex number
1046:
1043:
1005:
1004:
1003:
1002:
991:
985:
982:
979:
972:
969:
963:
959:
956:
953:
946:
943:
939:
934:
931:
911:
910:
909:
895:
892:
886:
882:
876:
872:
850:
847:
846:
845:
828:
814:
813:
807:+ 9807 Pa/m ×
804:
759:
758:
747:
736:
701:
700:
693:
670:
630:
629:
609:
598:
571:
552:
541:
514:
494:speed of light
484:, are denoted
473:
470:
452:
424:
400:
376:
352:
328:
304:
257:Greek alphabet
252:
249:
237:
236:
230:
207:
204:
200:
199:
190:
161:
160:
137:
126:
107:
104:
88:
85:
65:
64:
48:
47:
30:
29:
24:
13:
10:
9:
6:
4:
3:
2:
9213:
9202:
9199:
9198:
9196:
9173:
9172:
9167:
9152:
9151:
9145:
9142:
9140:9780226104201
9137:
9133:
9132:
9126:
9114:
9109:
9105:
9099:
9091:
9089:0-88318-642-X
9086:
9079:
9078:
9073:
9072:
9067:
9057:
9053:
9049:
9043:
9038:
9030:
9023:
9020:
9016:
9013:
9009:
9005:
9001:
8997:
8993:
8989:
8985:
8978:
8975:
8972:
8966:
8963:
8956:
8952:
8951:Help:template
8949:
8947:
8944:
8943:
8939:
8934:
8930:
8926:
8923:
8922:
8921:
8918:
8916:
8912:
8911:
8906:
8902:
8897:
8895:
8891:
8883:
8878:
8874:
8871:
8867:
8863:
8859:
8856:
8852:
8849:
8848:string theory
8845:
8841:
8836:
8832:
8829:
8828:
8826:
8822:
8821:
8820:
8813:
8809:
8805:
8801:
8797:
8794:
8791:
8787:
8784:
8783:
8782:
8778:
8774:
8766:
8761:
8756:
8753:
8752:
8751:
8749:
8745:
8741:
8737:
8733:
8729:
8720:
8718:
8715:
8714:
8711:
8709:
8706:
8702:
8699:
8698:
8695:
8693:
8691:
8687:
8683:
8680:
8679:
8676:
8674:
8672:
8669:
8668:
8664:
8661:
8658:
8657:
8654:
8648:
8643:
8639:
8635:
8634:
8630:
8627:
8623:
8619:
8615:
8611:
8607:
8604:
8603:
8602:
8595:
8591:
8583:
8580:
8576:
8574:
8570:
8567:
8566:
8562:
8559:
8556:
8552:
8550:
8547:
8544:
8543:
8540:
8536:
8532:
8528:
8524:
8516:
8512:
8504:
8496:
8491:
8489:
8486:
8485:
8482:
8478:
8473:
8468:
8462:
8458:
8456:
8453:
8452:
8448:
8445:
8442:
8438:
8434:
8430:
8428:
8425:
8424:
8420:
8417:
8414:
8410:
8406:
8404:
8401:
8400:
8396:
8392:
8389:
8386:
8382:
8375:
8364:
8361:
8357:
8353:
8349:
8346:
8345:
8342:
8334:
8330:
8321:
8312:
8310:
8306:
8303:
8302:
8299:
8295:
8291:
8288:
8285:
8284:
8278:
8272:
8268:
8264:
8261:
8258:
8254:
8252:
8249:
8248:
8244:
8241:
8238:
8235:
8231:
8227:
8225:
8224:Cross product
8222:
8221:
8217:
8214:
8211:
8208:
8204:
8200:
8198:
8195:
8194:
8191:
8188:
8184:
8181:
8178:
8174:
8170:
8164:
8153:
8149:
8145:
8138:
8135:
8132:
8131:
8128:
8124:
8120:
8113:
8105:
8097:
8094:
8090:
8086:
8085:
8082:
8077:
8074:
8072:
8070:
8066:
8062:
8056:
8053:
8050:
8046:
8042:
8035:
8033:
8030:
8029:
8026:
8024:
8022:
8018:
8014:
8008:
8005:
8002:
7998:
7994:
7987:
7984:
7981:
7980:
7974:
7969:
7966:
7963:
7958:
7956:
7953:
7952:
7942:
7926:
7924:
7922:
7918:
7912:
7908:
7906:
7903:
7902:
7899:
7895:
7891:
7874:
7870:
7864:
7851:
7849:
7846:
7845:
7839:
7822:
7818:
7812:
7799:
7797:
7794:
7793:
7789:
7785:
7781:
7779:
7776:
7775:
7767:
7758:
7753:
7750:
7744:
7737:
7734:
7730:
7727:
7726:
7722:
7719:
7713:
7711:
7708:
7707:
7703:
7698:
7696:
7693:
7692:
7684:
7679:
7677:
7674:
7673:
7669:
7666:
7662:
7660:
7657:
7656:
7649:
7632:
7629:
7617:
7613:
7609:
7607:
7604:
7603:
7598:
7591:
7586:
7582:
7578:
7574:
7571:
7568:
7562:
7558:
7554:
7550:
7546:
7543:
7539:
7537:
7533:
7530:
7529:
7525:
7522:
7515:
7511:
7505:
7501:
7497:
7495:
7491:
7487:
7484:
7483:
7480:
7476:
7472:
7468:
7465:
7462:
7461:
7458:
7456:
7451:
7446:
7444:
7434:
7431:solutions to
7430:
7427:
7424:
7421:
7417:
7413:
7410:
7407:
7404:
7403:
7402:
7400:
7392:
7388:
7384:
7381:
7378:
7376:
7370:
7364:
7360:
7357:
7356:
7355:
7353:
7345:
7343:
7341:
7337:
7328:
7325:
7324:
7323:
7320:
7318:
7314:
7306:
7297:
7290:
7282:
7278:
7273:
7266:
7258:
7254:
7249:
7242:
7234:
7230:
7226:
7222:
7218:
7214:
7207:
7200:
7192:
7191:
7189:
7188:
7181:
7177:
7173:
7169:
7162:
7155:
7145:means "and",
7138:
7131:
7124:
7117:
7110:
7103:
7093:
7092:
7090:
7086:
7085:
7081:
7077:
7065:
7061:
7057:
7030:
7025:
7024:
7022:
7017:
7012:
7011:
6983:
6978:
6977:
6975:
6971:
6967:
6963:
6959:
6955:
6951:
6950:standing wave
6947:
6943:
6942:
6938:
6934:
6930:
6924:
6920:
6915:
6914:
6912:
6911:
6904:
6896:
6892:
6881:
6877:
6872:
6867:
6866:
6864:
6863:
6862:
6859:
6857:
6853:
6849:
6845:
6844:
6838:
6834:
6830:
6822:
6817:
6811:
6810:wave function
6807:
6802:
6801:
6800:
6793:
6792:wave function
6789:
6784:
6780:
6779:wave function
6776:
6772:
6767:
6766:
6765:
6763:
6753:
6749:
6745:
6741:
6740:String theory
6738:
6736:
6733:
6730:
6726:
6725:
6724:
6722:
6718:
6711:
6708:
6705:
6702:
6701:
6699:
6696:
6693:
6690:
6689:
6688:
6685:
6682:
6681:particle spin
6678:
6675:
6671:
6668:and possibly
6667:
6663:
6658:
6655:
6652:
6649:
6648:
6647:
6645:
6641:
6636:
6632:
6628:
6625:
6622:
6618:
6615:
6612:
6609:
6608:
6607:
6605:
6601:
6599:
6597:
6593:
6592:
6591:
6589:
6581:
6575:
6571:
6568:
6564:
6560:
6556:
6555:
6554:
6553:
6548:
6545:
6540:
6535:
6531:
6526:
6522:
6518:
6510:
6506:
6502:
6498:
6494:
6490:
6486:
6485:natural units
6483:
6480:
6476:
6473:
6472:
6471:
6469:
6461:
6458:
6455:
6454:
6453:
6451:
6448:" etc.), and
6447:
6443:
6439:
6428:
6426:
6424:
6421:
6420:
6417:
6415:
6413:
6409:
6405:
6402:
6400:
6397:
6396:
6393:
6391:
6389:
6385:
6381:
6377:
6374:
6372:
6369:
6368:
6365:
6363:
6361:
6357:
6353:
6349:
6345:
6342:
6340:
6337:
6336:
6333:
6331:
6329:
6325:
6322:
6320:
6317:
6316:
6313:
6310:
6308:
6306:
6303:
6301:
6298:
6297:
6293:
6291:
6287:
6285:
6282:
6279:
6278:
6275:
6274:
6273:
6264:
6261:
6258:
6255:
6252:
6250:
6247:
6246:
6242:
6238:
6235:
6233:
6230:
6227:
6225:
6222:
6221:
6218:
6215:
6212:
6209:
6206:
6204:
6201:
6200:
6196:
6194:
6190:
6188:
6185:
6182:
6181:
6178:
6177:
6176:
6170:
6168:
6166:
6162:
6158:
6154:
6150:
6146:
6142:
6134:
6132:
6130:
6129:summary style
6121:
6089:
6085:
6082:
6081:
6077:
6057:
6051:
6048:
6042:
6036:
6033:
6022:
6019:
6013:
6010:
6007:
6001:
5995:
5992:
5989:
5983:
5977:
5974:
5965:
5947:
5936:
5930:
5919:
5908:
5905:
5891:
5885:
5871:
5865:
5843:
5839:
5835:
5831:
5827:
5821:
5820:
5819:
5817:
5813:
5805:
5800:
5799:N, Q, Z, R, C
5795:
5743:
5740:ℕ, ℚ, ℤ, ℝ, ℂ
5737:
5736:
5735:
5733:
5729:
5721:
5716:
5698:
5693:
5688:
5684:
5681:
5675:
5672:
5667:
5663:
5659:
5656:
5647:
5646:
5645:
5614:
5610:
5596:
5592:
5588:
5568:
5565:
5560:
5556:
5552:
5549:
5540:
5539:
5538:
5536:
5488:
5484:
5481:
5480:
5478:
5477:
5396:
5395:
5393:
5390:
5333:
5330:
5329:
5328:
5314:
5308:
5300:
5297:
5293:
5290:
5283:
5276:
5275:
5271:
5269:
5268:has meaning.
5262:
5258:
5254:
5249:
5243:
5235:
5229:
5223:
5216:
5208:
5196:
5188:
5180:
5179:
5178:
5175:
5158:
5151:
5143:
5132:
5124:
5112:
5104:
5096:
5089:
5081:
5073:
5072:
5070:
5067:
5066:
5064:
5061:
5054:
5046:
5038:
5035:
5030:
5024:
5020:
5016:
5011:
5010:
5006:
5002:
4999:
4995:
4989:
4983:
4973:
4965:
4957:
4954:
4948:
4943:
4942:
4938:
4935:
4932:
4931:
4928:
4927:
4926:
4920:
4916:
4913:
4909:
4905:
4902:
4898:
4897:
4896:
4893:
4887:
4882:
4859:
4856:
4851:
4848:
4841:
4838:
4831:
4830:
4829:
4826:
4820:
4815:
4811:
4807:
4803:
4797:
4789:
4783:
4777:
4772:
4754:
4750:
4747:
4739:
4736:
4733:
4727:
4724:
4721:
4718:
4710:
4707:
4704:
4698:
4694:
4688:
4681:
4670:
4660:
4659:
4657:
4656:
4637:
4634:
4626:
4623:
4620:
4614:
4611:
4608:
4605:
4597:
4594:
4591:
4585:
4580:
4573:
4563:
4559:
4555:
4551:
4547:
4543:
4539:
4535:
4531:
4521:
4520:
4518:
4514:
4510:
4506:
4505:
4501:
4497:
4496:
4479:
4476:
4460:
4455:
4448:
4438:
4434:
4429:
4420:
4419:
4417:
4412:
4406:
4398:
4394:
4390:
4384:
4377:
4370:
4363:
4362:
4358:
4357:
4337:
4331:
4328:
4325:
4320:
4315:
4312:
4309:
4301:
4295:
4292:
4282:
4278:
4275:
4268:
4264:
4260:
4253:
4252:
4250:
4249:
4228:
4218:
4210:
4207:
4200:
4183:
4179:
4170:
4166:
4160:
4157:
4156:
4147:
4132:
4123:
4117:
4116:Four gradient
4114:
4113:
4107:
4100:
4097:
4096:
4092:
4086:
4085:
4082:
4081:
4075:
4070:
4064:
4060:
4043:
4039:
4031:
4030:
4028:
4012:
4004:
3999:
3994:
3990:
3987:
3971:
3964:
3963:
3961:
3960:four gradient
3956:
3948:
3945:
3941:
3938:
3934:
3930:
3911:
3880:, use either
3878:
3877:
3873:
3854:
3832:
3820:
3815:
3793:
3781:
3776:
3754:
3742:
3729:
3725:
3718:
3702:
3698:
3691:
3675:
3671:
3664:
3647:
3646:
3644:
3643:
3622:
3608:
3589:
3583:
3569:
3550:
3544:
3530:
3511:
3495:
3480:
3476:
3468:
3453:
3449:
3441:
3426:
3422:
3416:
3415:
3413:
3410:
3406:
3402:
3399:
3395:
3391:
3390:differentials
3387:
3386:
3382:
3377:
3373:
3366:
3359:
3343:
3338:
3334:
3324:
3320:
3319:
3317:
3309:
3308:
3291:
3288:
3283:
3279:
3269:
3265:
3264:
3262:
3258:
3254:
3238:
3233:
3229:
3218:
3212:
3211:
3209:
3208:Lorentz group
3205:
3192:
3191:
3187:
3183:
3179:
3175:
3171:
3170:
3153:
3148:
3144:
3134:
3130:
3129:
3127:
3123:
3119:
3115:
3111:
3107:
3103:
3100:
3097:Letters that
3096:
3095:
3094:
3092:
3088:
3080:
3076:
3075:
3070:
3069:
3064:
3060:
3057:
3056:
3055:
3053:
3052:spinor fields
3049:
3048:tensor fields
3045:
3044:vector fields
3041:
3037:
3033:
3025:
3023:
3014:(without the
2999:
2995:
2987:
2986:
2985:
2956:
2951:
2943:
2942:
2941:
2930:
2926:
2925:
2924:
2919:
2912:
2908:
2907:its renderers
2904:
2902:<math: -->
2898:
2893:
2889:
2885:
2879:
2872:
2868:
2860:
2836:
2812:
2773:
2770:
2766:
2762:
2757:
2754:
2750:
2746:
2732:
2728:
2721:
2720:
2719:
2697:
2674:
2670:
2627:
2623:
2609:
2605:
2589:
2582:
2581:
2580:
2578:
2570:
2561:
2557:
2548:
2544:
2539:
2533:∇<sub: -->
2527:
2523:
2518:
2512:∂<sub: -->
2509:
2508:
2506:
2502:
2490:
2486:
2482:
2461:
2458:
2455:
2427:
2419:
2406:
2405:
2403:
2399:
2395:
2391:
2337:
2325:
2311:
2310:
2304:
2303:
2301:
2297:
2293:
2292:
2287:
2283:
2280:
2275:
2269:
2264:
2261:
2238:
2232:
2224:
2219:
2216:
2191:
2188:
2185:
2181:
2177:
2174:
2171:
2159:
2149:
2140:
2132:
2126:
2125:
2120:
2110:
2101:
2090:
2080:
2073:
2069:
2065:
2064:Hilbert space
2061:
2060:Quantum state
2058:
2039:
2031:
1999:
1993:
1972:
1967:
1966:
1964:
1960:
1956:
1935:
1931:
1928:
1922:
1917:
1914:
1881:
1880:
1849:
1844:
1843:
1841:
1840:
1836:In practice,
1835:
1779:
1771:
1762:
1755:
1748:
1747:
1742:
1741:
1731:
1713:
1686:
1674:
1671:
1667:
1664:
1663:
1661:
1657:
1656:
1652:
1628:
1625:
1622:
1614:
1598:
1592:
1586:
1565:
1555:
1547:
1542:
1538:
1534:
1528:
1525:
1516:
1507:
1499:
1498:
1496:
1473:
1466:
1463:
1460:
1452:
1441:
1437:
1431:
1420:
1402:
1392:
1389:
1386:
1382:
1378:
1372:
1369:
1360:
1351:
1343:
1342:
1340:
1322:
1314:
1307:
1304:
1301:
1293:
1282:
1278:
1274:
1271:
1266:
1260:
1242:
1232:
1224:
1219:
1215:
1211:
1208:
1205:
1199:
1196:
1187:
1178:
1170:
1169:
1168:
1167:
1163:
1159:
1155:
1154:
1146:
1142:
1141:
1122:
1119:
1116:
1112:
1108:
1103:
1099:
1095:
1092:
1089:
1086:
1082:
1074:
1073:
1071:
1067:
1066:
1065:
1063:
1060:
1056:
1052:
1044:
1042:
1040:
1039:
1034:
1030:
1026:
1022:
1018:
1014:
1010:
989:
983:
977:
967:
961:
957:
951:
944:
941:
937:
929:
922:
921:
919:
915:
912:
893:
890:
880:
874:
862:
861:
859:
856:
855:
854:
848:
842:
838:
834:
827:
823:
819:
818:
817:
810:
803:
799:
795:
794:
793:
791:
786:
781:
774:
773:
768:
764:
752:
748:
741:
737:
730:
726:
725:
724:
722:
721:
711:
706:
698:
694:
691:
687:
683:
679:
675:
671:
668:
664:
656:
653:
652:
651:
649:
648:
643:
642:
637:
636:
608:
603:
599:
581:
576:
572:
551:
546:
542:
524:
519:
515:
500:
495:
491:
490:
489:
487:
483:
479:
471:
469:
450:
422:
398:
374:
350:
326:
302:
291:
286:
284:
283:general style
279:<math: -->
275:
270:
261:<math: -->
258:
251:Greek letters
250:
248:
246:
242:
234:
231:
228:
224:
221:
220:
219:
217:
213:
205:
203:
197:
191:
188:
185:template for
181:
174:
173:
172:
170:
166:
155:
145:
138:
135:
131:
127:
124:
123:<math: -->
120:
117:
116:
115:
112:
105:
102:
98:
94:
86:
84:
82:
78:
74:
70:
63:
61:
57:
52:
51:
44:
40:
36:
35:
28:
25:
18:
17:
9179:. Retrieved
9170:
9158:. Retrieved
9149:
9130:
9119:February 28,
9117:. Retrieved
9076:
9055:
9051:
9047:
9034:
9028:
9022:
8994:(1): 65–76,
8991:
8987:
8977:
8970:
8965:
8929:edit notices
8919:
8909:
8898:
8887:
8865:
8854:
8843:
8825:wavefunction
8817:
8808:"references"
8799:
8795:
8789:
8785:
8780:
8771:Main pages:
8725:
8652:
8631:
8605:
8600:
8589:
8586:
8578:
8557:
8554:
8530:
8526:
8522:
8514:
8510:
8502:
8494:
8471:
8466:
8460:
8440:
8436:
8432:
8412:
8408:
8394:
8384:
8380:
8373:
8332:
8328:
8319:
8259:
8256:
8233:
8229:
8206:
8202:
8186:
8176:
8172:
8168:
8162:
8151:
8147:
8143:
8122:
8118:
8111:
8103:
8068:
8064:
8060:
8057:
8054:
8048:
8044:
8040:
8037:
8020:
8016:
8012:
8009:
8006:
8000:
7996:
7992:
7989:
7972:
7961:
7940:
7920:
7916:
7914:
7910:
7783:
7765:
7756:
7748:
7742:
7729:Square roots
7715:
7701:
7682:
7664:
7615:
7611:
7596:
7590:real numbers
7584:
7580:
7576:
7569:
7566:
7560:
7556:
7552:
7548:
7544:
7541:
7520:
7513:
7509:
7503:
7499:
7454:
7449:
7442:
7438:
7416:EM radiation
7396:
7374:
7363:real numbers
7351:
7349:
7332:
7321:
7316:
7310:
7292:
7285:
7280:
7276:
7268:
7261:
7256:
7252:
7244:
7237:
7232:
7228:
7224:
7220:
7216:
7209:
7202:
7195:
7179:
7175:
7171:
7164:
7157:
7150:
7133:
7126:
7119:
7112:
7105:
7098:
7080:less clearer
7079:
7063:
7059:
7055:
7028:
7015:
6981:
6973:
6946:normal modes
6936:
6935:the context
6932:
6918:
6903:real numbers
6901:denotes the
6879:
6875:
6870:
6860:
6855:
6851:
6847:
6840:
6828:
6826:
6809:
6798:
6791:
6778:
6762:wavefunction
6759:
6727:Variants of
6719:
6686:
6673:
6642:
6602:
6594:
6587:
6585:
6574:use SI units
6573:
6566:
6562:
6558:
6551:
6550:
6543:
6538:
6533:
6529:
6520:
6516:
6514:
6488:
6467:
6466:In general,
6465:
6435:
6271:
6174:
6164:
6160:
6156:
6138:
6125:
6087:
5837:
5833:
5829:
5825:
5810:Symbols for
5809:
5798:
5725:
5644:rather than
5643:
5532:
5326:
5267:
5260:
5256:
5252:
5247:
5241:
5233:
5227:
5221:
5214:
5206:
5194:
5186:
5173:
5170:
5156:
5149:
5141:
5130:
5122:
5110:
5102:
5094:
5087:
5079:
5059:
5052:
5044:
5033:
5022:
5018:
5014:
5007:derivatives
5004:
4997:
4993:
4987:
4981:
4971:
4963:
4952:
4946:
4924:
4891:
4885:
4880:
4878:
4824:
4818:
4813:
4799:
4781:
4775:
4668:
4561:
4557:
4553:
4549:
4545:
4541:
4537:
4533:
4529:
4512:
4507:There is an
4499:
4436:
4432:
4427:
4415:
4410:
4404:
4396:
4280:
4276:
4273:
4266:
4262:
4258:
4168:
4164:
4121:
4093:Recommended
4068:
4062:
3992:
3951:
3936:
3932:
3727:
3723:
3716:
3700:
3696:
3689:
3673:
3669:
3662:
3493:
3478:
3474:
3466:
3451:
3447:
3439:
3424:
3420:
3404:
3397:
3322:
3267:
3216:
3181:
3177:
3173:
3132:
3098:
3084:
3072:
3066:
3029:
3021:
2983:
2938:
2928:
2899:
2891:
2887:
2883:
2877:
2870:
2866:
2858:
2856:
2730:
2726:
2718:rather than
2717:
2587:
2574:
2559:
2555:
2546:
2542:
2537:
2525:
2521:
2516:
2308:
2307:
2290:
2289:
2285:
2284:For tensors
2273:
2267:
2157:
2147:
2138:
2130:
1970:
1965:the arrows:
1962:
1959:unit vectors
1878:
1877:
1847:
1838:
1837:
1769:
1760:
1745:
1744:
1739:
1738:
1665:
1144:
1069:
1048:
1036:
1006:
852:
840:
836:
832:
825:
821:
815:
808:
801:
797:
787:
770:
760:
751:electronvolt
718:
709:
705:atomic units
702:
689:
685:
681:
678:the units of
677:
645:
639:
633:
631:
606:
579:
549:
522:
498:
475:
289:
287:
276:
254:
238:
232:
226:
222:
209:
201:
195:
186:
168:
164:
162:
113:
109:
66:
55:
53:
43:village pump
32:
26:
8917:for this).
8910:Gravitation
8549:composition
8362:integrals)
8350:(including
8271:row vectors
8197:Dot product
8079:Elementary
7968:multivalued
7932:for scalar
7490:Subtraction
7439:etc., then
6954:diffraction
6923:real number
6850:to replace
6841:especially
6818:Mathematics
6666:world lines
6598:(all types)
6489:fundamental
6290:SI prefixes
6193:SI prefixes
5722:Number sets
4933:Operations
4806:derivatives
4005:The symbol
3949:The symbol
3394:derivatives
2976:applied to
2485:dot product
2483:The use of
2394:contraction
1839:bold italic
1735:</u: -->
1711:underlining
1021:integration
285:for names.
165:consistency
136:characters,
8927:decide if
8877:categories
8804:"see also"
8659:Operation
8286:Operation
8089:derivative
7475:Arithmetic
7463:Operation
7389:discussed
7313:operations
6629:(includes
6547:factor...
6214:centimetre
5812:Lie groups
5806:Lie groups
5327:Examples:
5296:WP:MOSCHEM
4881:derivative
4794:See also:
3360:Note that
2404:notation:
2400:, not the
2279:eigenvalue
1789:overlining
1734:<u: -->
1730:diacritics
1684:overarrows
1670:diacritics
1062:generators
853:Examples:
647:dimensions
635:quantities
245:nitpicking
159:templates.
91:See also:
81:WP:MOSCHEM
77:WP:MOSMATH
9098:cite book
8957:Footnotes
8814:sections.
8796:navboxes:
8786:sidebars:
8740:operators
8732:manifolds
8662:Notation
8447:Euclidean
8419:Euclidean
8289:Notation
8243:Euclidean
8216:Euclidean
8134:Integrals
8087:Ordinary
7796:Summation
7778:Factorial
7733:nth roots
7594:"vector"
7466:Notation
7336:tetration
7194:"Letting
6889:denotes "
6858:at hand.
6596:Mechanics
6517:which one
6491:physics;
5814:shall be
4936:Notation
4405:including
4388:template.
3263:letters:
3128:letters:
3122:spacetime
2263:Operators
1149:\frac{}{}
1045:Functions
1017:summation
753:, symbol
742:, symbol
731:, symbol
478:variables
223:variables
214:) versus
198:formulae.
196:displayed
189:formulae,
169:consensus
101:WP:«math»
39:talk page
9195:Category
8940:See also
8861:needed).
8844:abstract
8800:very end
8395:Advanced
8081:calculus
7606:Division
7486:Addition
7359:Integers
7275:), then
6970:ellipsis
6933:explains
6885:, where
6752:M theory
6748:D-branes
6588:academic
6468:SI units
6399:pressure
6339:momentum
6319:velocity
6288:Decimal
6254:kilogram
6191:Decimal
6157:distance
6145:distance
5029:function
4908:operator
4901:limiting
4393:boundary
4087:Setting
3645:and not
3405:in front
3383:Calculus
2911:neutrino
2724:}}": -->
2585:}}": -->
1963:replaces
816:but not
9181:2 March
9160:1 March
9015:0465032
8996:Bibcode
8638:Fourier
8356:surface
8267:column-
8067:, coth
8063:, sech
8059:cosech
8047:, tanh
8043:, cosh
7970:unless
7938:either
7936:only(?)
7848:Product
7754:either
7383:decimal
7251:), and
6891:element
6856:physics
6806:physics
6775:physics
6750:", or "
6284:SI unit
6239:(min),
6187:SI unit
6135:Physics
5392:β decay
5003:Ratios
4779:" and "
4383:intmath
3206:of the
3110:spinors
3106:tensors
3102:indices
3054:) are:
3040:spinors
3036:tensors
3032:vectors
3016:\mathrm
2974:\mathrm
2501:tensors
2119:bra-ket
1013:tensors
1009:vectors
831:+ 9807
717:) (see
655:Voltage
290:variant
229:, while
134:Unicode
73:physics
8969:JCGM,
8810:, and
8665:Notes
8360:volume
8358:, and
8292:Notes
8019:, cot
8015:, sec
8011:cosec
7999:, tan
7995:, cos
7761:(then
7469:Notes
7141:where
7051:...},
7031:∈ {0,
6948:for a
6831:(i.e.
6812:is ...
6794:is ...
6781:is ...
6672:, but
6511:etc.),
6300:energy
6237:minute
6229:second
6203:length
5847:": -->
5828:), SO(
5747:": -->
3902:\nabla
3398:italic
3050:, and
3042:(also
3038:, and
2972:(with
2792:": -->
2739:": -->
2655:": -->
2598:": -->
2551:, not
2497:(0, 1)
2495:- and
2493:(1, 0)
2444:, not
2360:, not
2206:, not
2089:rangle
2079:langle
2019:, not
1874:, not
1147:, not
740:dalton
663:italic
644:, and
569:10 F⋅m
539:10 J⋅s
443:": -->
415:": -->
391:": -->
367:": -->
343:": -->
319:": -->
295:": -->
227:italic
216:italic
187:inline
99:, and
9175:(PDF)
9154:(PDF)
9081:(PDF)
8738:from
8539:above
8481:above
8309:nabla
8187:Basic
8091:(see
8039:sinh
7975:: -->
7770:≥ 0),
7731:(and
7619:or
7406:waves
7397:When
7391:above
7227:, if
7125:) ⇒ (
7111:) ∧ (
7062:/2 :
7041:, 1,
6994:, 1,
6984:= 0,
6974:three
6964:, or
6921:is a
6893:of a
6882:: -->
6878:∈ ℝ:
6712:(QCD)
6706:(QED)
6559:could
6557:They
6446:knots
6422:etc.
6371:force
6256:(kg)
6243:(h),
6216:(cm)
6208:metre
6114:, or
6078:Other
5836:), O(
5816:Roman
5027:as a
4910:(cf.
4814:ratio
4198:etc.
4145:etc.
3904:) or
3261:Latin
3126:Greek
3079:basis
3065:(cf.
1059:group
918:below
763:roman
697:roman
661:, an
641:units
626:10 kg
615:9.109
585:1.602
558:8.854
528:1.054
388:, or
233:names
212:roman
119:LaTeX
9183:2013
9162:2013
9136:ISBN
9121:2013
9104:link
9085:ISBN
8775:and
8726:...
8716:...
8640:and
8537:see
8519:,
8507:,
8499:,
8352:line
8269:and
7991:sin
7588:are
7477:and
7447:(or
7371:and
7361:and
7317:some
7299:)."
7279:and
7259:(so
7235:(so
7073:etc.
6960:and
6808:, a
6790:, a
6777:, a
6746:", "
6659:(GR)
6653:(SR)
6565:and
6521:many
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6262:(g)
6260:gram
6249:mass
6241:hour
6231:(s)
6224:time
6210:(m)
6165:mass
6161:time
6153:mass
6151:and
6149:time
5676:9807
5611:<
5569:9807
5533:The
5307:math
5287:and
4950:and
4369:math
4364:For
3650:∇ =
3419:∇ =
3312:i, j
3176:and
3116:and
3104:for
3071:and
2918:math
2789:,
2763:<
2736:,
2624:<
2595:,
2487:and
2392:For
2271:vs.
2084:and
1777:etc.
1672:, or
1666:bold
1658:For
1160:and
1011:and
788:The
749:the
738:the
727:the
674:volt
672:The
622:(28)
620:7139
600:the
595:10 C
573:the
565:(14)
563:8188
543:the
516:the
492:the
480:and
412:vs.
364:vs.
316:vs.
269:math
255:The
194:for
180:math
167:and
154:mvar
149:and
144:math
139:the
130:HTML
9004:doi
8903:in
8855:lot
8746:on
8730:on
8628:...
8608:or
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8470:...
8464:...
8367:∫∫∫
8339:, ∇
7960:ln
7945:or
7943:≥ 0
7759:≥ 0
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7182:."
7070:},
7066:∈ ℕ
7058:∈ {
7053:or
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6956:in
6895:set
6848:not
6804:In
6786:In
6769:In
6567:why
6563:how
6537:",
6505:QFT
6438:erg
6406:or
6378:or
6350:or
6163:or
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5370:→ 2
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5031:of
4883:of
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4066:or
3732:or
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2302:).
2109:ket
2100:bra
1905:,
1754:vec
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1272:exp
1209:exp
1015:),
780:val
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684:so
617:383
590:634
587:176
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533:817
530:571
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509:458
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8112:dx
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7861:∏
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7023::
6905:"
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6835:,
6674:no
6635:EM
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6532:=
6507:,
6503:,
6501:QM
6499:,
6497:GR
6495:,
6493:SR
6479:EM
6404:Pa
6380:kg
6352:kg
6312:eV
6167:.
6159:,
6147:,
6090:,
6086::
5615:ρ
5597:ρ
5507:+
5489:+
5485:→
5452:+
5434:+
5425:Cm
5421:96
5415:→
5406:Am
5402:95
5352:+
5334::
5310:}}
5304:{{
5285:}}
5279:{{
5263:,
5261:∂x
5257:∂F
5255:,
5248:∂x
5238:,
5234:∂x
5228:∂F
5224:,
5215:∂x
5201:,
5195:∂x
5187:∂F
5174:∂x
5150:dx
5131:dx
5111:dx
5097:=
5088:dx
5053:dx
5017:=
5005:or
4998:dx
4994:dy
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4972:dx
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4839:ρ
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4386:}}
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4229:α
4225:∂
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4040:◻
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3972:◻
3912:▽
3888:∇
3848:^
3830:∂
3826:∂
3809:^
3791:∂
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3770:^
3752:∂
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3509:∇
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3000:ν
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2628:ρ
2610:ρ
2554:(∇
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2242:^
2239:ψ
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2163:,
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1792:¯
1768:,
1757:}}
1751:{{
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