en.wikipedia.org website review
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en.wikipedia.org is 60% geoptimaliseerd!
SEO Keyword summary for en.wikipedia.org/wiki/second_quantization
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be psi
Focus keyword
Short and long tail
Short Tail Keywords psi alpha displaystyle |
long Tail Keywords (2 words) psi alpha wave function alpha otimes 1psi 2psi annihilation operators |
long Tail Keywords (3 words) creation and annihilation psi alpha otimes many-body wave function 1psi 2psi 1psi single-particle state displaystyle displaystyle psi alpha state displaystyle alpha |
en.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a en.wikipedia.org/wiki/second_quantization page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
Title length
second quantization wikipedia
Meta description
Meta description legth
Meta description SEO
No meta relevance in the description detected !
Content SEO
Number of Words
Spam detected?
Headings
Heading distribution
Heading normalisation
Heading SEO impact
Emphasis (bold and italic)
Emphasis SEO impact
Images
Number of images
Images dimensions
Image alt descriptions
Images SEO impact
wikipedia free encyclopedia displaystyle mathbf ileftrightarrow psi bcdots icdots jcdots fcdots alpha iprod npsi imathbf iequiv otimes cdots irangle mathcal bmathbf imathcal nmathcal spsi nsum snprod snpsi fmathbf apsi prod uijpsi jmathbf langle ialpha jrangle bmathcal noperatorname perm fmathcal ndet nalpha rangle equiv textstyle sum begincases textfermions textbosonsendcases sqrt nprod tfrac bleftfrac right sbigotimes limits ffrac abigotimes oslash quad beta delta balpha dagger neq frac beginarrayrlb leftfrac rightfrac endarray rightpsi hat nbeta ngamma bbeta xalpha palpha mathrm hbar pbeta xbeta calpha beginarrayrlc cbeta chi textrecalpha textimcalpha ichi jdelta anu cnu bnu leftmathbf rightanu leftpsi rightdelta over vsum eimathbf kcdot amathbf wikimedia foundation powered mediawiki
Mobile SEO en.wikipedia.org/wiki/second_quantization
Mobile rendering
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Mobile optimizations
Responsive design detected (mobile css)
No flash detected !
Mobile improvement
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Marketing / lead generation for en.wikipedia.org/wiki/second_quantization
Social Media
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Conversion form
Search form
Analytics
Online presence
SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
quantization found in path !
second found in path !
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
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Favicon icon found?
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Robots.txt found?
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Sitemap found?
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Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
statistics
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httpsenwikipediaorgwindexphptitlesecondquantizationoldid1160875914
page information
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wiki read
quantum field theory
feynman diagram
history
field theory
electromagnetism
weak force
strong force
quantum
special relativity
general relativity
gauge theory
yangmills theory
symmetries
symmetry in quantum mechanics
csymmetry
psymmetry
tsymmetry
lorentz symmetry
poincar symmetry
gauge symmetry
explicit symmetry breaking
spontaneous symmetry breaking
noether charge
topological charge
anomaly
background field method
brst quantization
correlation function
crossing
effective action
effective field theory
expectation value
lattice field theory
lsz reduction formula
partition function
propagator
quantization physics
regularization
renormalization
vacuum state
wicks theorem
dirac equation
kleingordon equation
proca equations
wheelerdewitt equation
bargmannwigner equations
standard model
quantum electrodynamics
electroweak interaction
quantum chromodynamics
higgs mechanism
string theory
supersymmetry
technicolor
theory of everything
quantum gravity
adler
anderson
anselm
bargmann
becchi
belavin
bell
berezin
bethe
bjorken
bleuer
bogoliubov
brodsky
brout
buchholz
cachazo
callan
coleman
dashen
dewitt
paul dirac
doplicher
dyson
englert
faddeev
fadin
fayet
fermi
feynman
fierz
vladimir fock
frampton
fritzsch
frhlich
fredenhagen
furry
glashow
gelfand
gellmann
glimm
goldstone
gribov
gross
gupta
guralnik
haag
heisenberg
hepp
higgs
hagen
t hooft
iliopoulos
ivanenko
jackiw
jaffe
jonalasinio
pascual jordan
jost
kendall
kinoshita
klebanov
kontsevich
kuraev
landau
lee
lehmann
leutwyler
lipatov
opuszaski
low
lders
maiani
majorana
maldacena
mller
naimark
nambu
neveu
nishijima
oehme
oppenheimer
osterwalder
parisi
pauli
peskin
plefka
polyakov
pomeranchuk
popov
proca
rubakov
ruelle
salam
schrader
schwarz
schwinger
segal
seiberg
semenoff
shifman
shirkov
skyrme
sommerfield
stora
stueckelberg
sudarshan
symanzik
thirring
tomonaga
tyutin
vainshtein
veltman
ward
weinberg
weisskopf
wentzel
wess
wetterich
weyl
wick
wightman
wigner
wilczek
wilson
witten
yang
yukawa
zamolodchikov
zamolodchikov
zee
zimmermann
zinnjustin
zuber
zumino
manybody
canonical quantization
field operators
first quantization
fock state
creation and annihilation operators
indistinguishability
statistics
bosons
fermions
permanent
determinant
antisymmetrizer
symmetric group
permutation
permutation sign
slater determinant
pauli exclusion principle
fock space
hilbert space
quantum harmonic oscillator
tensor algebra
kronecker delta
jordanwigner string
spin structure
qubit
majorana fermion
clifford algebra
real space representation
quantum
operators
wavefunctions
quantum field
fourier basis
schrdinger wave function
dirac spinor
semiclassical
geometric quantization
schrdinger functional
scalar field theory
bibcode
s2cid
reed michael
simon barry
isbn
arxiv
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Links to external pages
Outloing links
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SEO Advice for en.wikipedia.org
In this section we provide pointers on how you can to optimize your web page so it can be found more easily by search engines and how to make it rank higher by optimizing the content of the page itself. For each of the individual criteria the maximum score is 100%. A score below 70% is considered to be indication that the page is not complying with general SEO standards and should be evaluated and/or fixed. Not every factor is weighted the same and some are not as important as others. Relatively unimportant factors like meta keywords are not included in the overall score.
Item | Factor | Pointers | |
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PageTitle | 100% | Far too many sites lack a page title. A page title is the first thing that shows in the search results so always use the title element. | |
Title relevance | 87% | A title should reflect the contents of a site. This site has a 67 % match | |
Title Length | 80% | Limit your title to anywhere between 40 and 70 characters. Your title was 32 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
Meta description relevance | 0% | Meta Description should reflect the contents of a site. This site has a 0 % match | |
Number of internal links | 30% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 315 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 3 level 1 folders and 6 folders above or in the first level of navigation. | |
Headings | 100% | Headers should reflect the contents of a site. This site has a 47 % match | |
Links | 10% | Link anchors should to some degree reflect the contents of a site. This site has a 5 % match | |
Image alt tags | 36% | Image alt tags should to some degree reflect the contents of a site. This site has a 13 % match | |
Bold and italic | 42% | Bold and italic tags should reflect the contents of a site to some degree. This site has a 14 % match | |
Html ratio | 30% | Try to keep the html / text ratio as low as possible. More html means longer loading times. Layout should be handled in a serpate css file | |
Image descriptions | 98% | 97.619047619048 % of all images have been described via the "alt" attribute. Describing images with relevant text may lead to better results in the search engines. | |
Page errors | 100% | Pages with no errors display significantly faster on most browsers. We detected 0 errors and warnings | |
WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 5540 words | |
Server response time | 100% | A fast server speeds up a website. This server responds 90.14% faster then average | |
Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 30% | There are no important keywords in your domain name | |
Keywords in domain path | 100% | There are important keywords in the domain path | |
Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 335 inline style declarations ( <a style="color:green">) with a size of 11690 bytes | |
Excessive use of the same words | 100% | There is no indication that there are one or more keywords that are used excessively. | |
Frames or iframes | 100% | Perfect, detected not (i)frames on your webpagina | |
Flash | 100% | Perfect, we detected no flash objects on your page | |
Css | 30% | We detected too much (2) CSS files on your page. Css files block the loading of a webpage. | |
Javascript | 100% | Perfect, we did not detect too many blocking JavaScript files | |
Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
Most important heading | 100% | Perfect, we detected a correct use of the most important (h1) heading! | |
Normalized headings | 40% | We dit not font a normalized heading structure. A heading 2 (h2) for example should be followed by a heading of an equal level (h2), a child heading (h3) or even a aprent heading (h1). |
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en.wikipedia.org images and descriptions
126 images found at en.wikipedia.org Images can improve the user experience for a website by making a pag visually appealing Images can also add extra keyword relevance to a webpage by using alt tags. Images can also slow down a website. If the width and height for a picture is not specified for a browser know in advance how large the image is. A browser must first load the picture and see before it knows how much space should be on the page. Upon reservation In the meantime, the browser can do little but wait. When the height and width for the plate are given in the HTML code, a browser just continues to build for a page while the images load in the background.
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2407d841dce5edeb776a55257b99b21fb373e2be height: height attribute not set width: width attribute not set description: {\displaystyle {\tfrac {1}{\sqrt {n!}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/819f392dbb0ebea8383cf40ef2ab9ca86e0faa1c height: height attribute not set width: width attribute not set description: {\displaystyle |[n_{\alpha }]\rangle _{\rm {b}}=\left({\frac {1}{n!\prod _{\alpha }n_{\alpha }!}}\right)^{1/2}{\mathcal {s}}\bigotimes \limits _{\alpha }\psi _{\alpha }^{\otimes n_{\alpha }}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8ba48c4ff2d4244f8b5549dc89e83f03bd893d11 height: height attribute not set width: width attribute not set description: {\displaystyle |[n_{\alpha }]\rangle _{\rm {f}}={\frac {1}{\sqrt {n!}}}{\mathcal {a}}\bigotimes \limits _{\alpha }\psi _{\alpha }^{\otimes n_{\alpha }}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/661a7415c222881b49a4acab7f1a553629e8ca0b height: height attribute not set width: width attribute not set description: {\displaystyle n_{\alpha }=0,1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/47d64fcfc7af17f1cecb0a127546e9c7aca5a0a4 height: height attribute not set width: width attribute not set description: {\displaystyle \psi _{\alpha }\equiv 1\otimes \psi _{\alpha }\equiv \psi _{\alpha }\otimes 1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/50af36f1f34134af96dd6280949eb615e61423c1 height: height attribute not set width: width attribute not set description: {\displaystyle \psi =\psi _{\alpha _{1}}\otimes \psi _{\alpha _{2}}\otimes \cdots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/934bbdb820a982d74e1b3239cdbbd469636bd73a height: height attribute not set width: width attribute not set description: {\displaystyle \otimes _{\pm }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b278e4019dfe2d733ba000aecc3f7fd31e10c3a8 height: height attribute not set width: width attribute not set description: {\displaystyle \oslash _{\pm }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/26a2035b36e5e1c0c647143fbe0dbe7b7104029a height: height attribute not set width: width attribute not set description: {\displaystyle \psi _{\alpha }\otimes _{\pm }1=\psi _{\alpha },\quad \psi _{\alpha }\otimes _{\pm }(\psi _{\beta }\otimes \psi )=\psi _{\alpha }\otimes \psi _{\beta }\otimes \psi \pm \psi _{\beta }\otimes (\psi _{\alpha }\otimes _{\pm }\psi );} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/23c285094d208719c75d462fc624a206503fdd66 height: height attribute not set width: width attribute not set description: {\displaystyle \psi _{\alpha }\oslash _{\pm }1=0,\quad \psi _{\alpha }\oslash _{\pm }(\psi _{\beta }\otimes \psi )=\delta _{\alpha \beta }\psi \pm \psi _{\beta }\otimes (\psi _{\alpha }\oslash _{\pm }\psi ).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/12656c1c39d2ddb970601b3f4458023baa011084 height: height attribute not set width: width attribute not set description: {\displaystyle \delta _{\alpha \beta }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ef6894a6c2f414b03c984a1c7f0639063b0020ab height: height attribute not set width: width attribute not set description: {\displaystyle \alpha =\beta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/869e366caf596564de4de06cb0ba124056d4064b height: height attribute not set width: width attribute not set description: {\displaystyle \pm } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b3aa31d48819ad11601d402dbabcf5a607738cb9 height: height attribute not set width: width attribute not set description: {\displaystyle b_{\alpha }^{\dagger }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fbfba2ff3a4a7b22f2847c829622c28fc5d146d6 height: height attribute not set width: width attribute not set description: {\displaystyle b_{\alpha }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/750cbf5241c80560ce93b947b23a8eff5be83808 height: height attribute not set width: width attribute not set description: {\displaystyle b_{\alpha }\neq b_{\alpha }^{\dagger }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6a2b9e5768efaa7368058004d3bd2083dd175037 height: height attribute not set width: width attribute not set description: {\displaystyle b_{\alpha }^{\dagger }\psi ={\frac {1}{\sqrt {n+1}}}\psi _{\alpha }\otimes _{+}\psi ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2a0aea08cabec5db50431c3d8926d5e6f6ba8934 height: height attribute not set width: width attribute not set description: {\displaystyle b_{\alpha }\psi ={\frac {1}{\sqrt {n}}}\psi _{\alpha }\oslash _{+}\psi ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a535a878d496141e68076c776925b1185d531a94 height: height attribute not set width: width attribute not set description: {\displaystyle \psi _{\alpha }\otimes _{+}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fdf2b9cbfe9051fd4e7b50c8028866d497eac35b height: height attribute not set width: width attribute not set description: {\displaystyle n+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/be4e037e05708d178ce59bec224f74038ed5f2f4 height: height attribute not set width: width attribute not set description: {\displaystyle \psi _{\alpha }\oslash _{+}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3 height: height attribute not set width: width attribute not set description: {\displaystyle n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c03a5c6bb5472965804c5a17e7fd8da16417740e height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{rl}b_{1}^{\dagger }|1_{1},1_{2}\rangle =&{\frac {1}{\sqrt {2}}}(b_{1}^{\dagger }\psi _{1}\psi _{2}+b_{1}^{\dagger }\psi _{2}\psi _{1})\\=&{\frac {1}{\sqrt {2}}}\left({\frac {1}{\sqrt {3}}}\psi _{1}\otimes _{+}\psi _{1}\psi _{2}+{\frac {1}{\sqrt {3}}}\psi _{1}\otimes _{+}\psi _{2}\psi _{1}\right)\\=&{\frac {1}{\sqrt {2}}}\left({\frac {1}{\sqrt {3}}}(\psi _{1}\psi _{1}\psi _{2}+\psi _{1}\psi _{1}\psi _{2}+\psi _{1}\psi _{2}\psi _{1})+{\frac {1}{\sqrt {3}}}(\psi _{1}\psi _{2}\psi _{1}+\psi _{2}\psi _{1}\psi _{1}+\psi _{2}\psi _{1}\psi _{1})\right)\\=&{\frac {\sqrt {2}}{\sqrt {3}}}(\psi _{1}\psi _{1}\psi _{2}+\psi _{1}\psi _{2}\psi _{1}+\psi _{2}\psi _{1}\psi _{1})\\=&{\sqrt {2}}|2_{1},1_{2}\rangle .\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1ae9060ea65787c3ab9b9320bd1256580f3b0d17 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{rl}b_{1}|2_{1},1_{2}\rangle =&{\frac {1}{\sqrt {3}}}(b_{1}\psi _{1}\psi _{1}\psi _{2}+b_{1}\psi _{1}\psi _{2}\psi _{1}+b_{1}\psi _{2}\psi _{1}\psi _{1})\\=&{\frac {1}{\sqrt {3}}}\left({\frac {1}{\sqrt {3}}}\psi _{1}\oslash _{+}\psi _{1}\psi _{1}\psi _{2}+{\frac {1}{\sqrt {3}}}\psi _{1}\oslash _{+}\psi _{1}\psi _{2}\psi _{1}+{\frac {1}{\sqrt {3}}}\psi _{1}\oslash _{+}\psi _{2}\psi _{1}\psi _{1}\right)\\=&{\frac {1}{\sqrt {3}}}\left({\frac {1}{\sqrt {3}}}(\psi _{1}\psi _{2}+\psi _{1}\psi _{2}+0)+{\frac {1}{\sqrt {3}}}(\psi _{2}\psi _{1}+0+\psi _{1}\psi _{2})+{\frac {1}{\sqrt {3}}}(0+\psi _{2}\psi _{1}+\psi _{2}\psi _{1})\right)\\=&\psi _{1}\psi _{2}+\psi _{2}\psi _{1}\\=&{\sqrt {2}}|1_{1},1_{2}\rangle .\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2f517186ed9e650e33d09028106fbfd07793b6a9 height: height attribute not set width: width attribute not set description: {\displaystyle |0_{\alpha }\rangle =1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c9c2bef2631a32950e61b5e8846b84cac3519379 height: height attribute not set width: width attribute not set description: {\displaystyle b_{\alpha }^{\dagger }|0_{\alpha }\rangle =\psi _{\alpha }\otimes _{+}1=\psi _{\alpha }=|1_{\alpha }\rangle ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/10db1d7c822aea8d2e92272ea498a4bd50f70258 height: height attribute not set width: width attribute not set description: {\displaystyle b_{\alpha }^{\dagger }|n_{\alpha }\rangle ={\frac {1}{\sqrt {n_{\alpha }+1}}}\psi _{\alpha }\otimes _{+}\psi _{\alpha }^{\otimes n_{\alpha }}={\sqrt {n_{\alpha }+1}}\psi _{\alpha }^{\otimes (n_{\alpha }+1)}={\sqrt {n_{\alpha }+1}}|n_{\alpha }+1\rangle .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/91cee27a5a6c63a7fd9f5423d749bad1ae6d8e01 height: height attribute not set width: width attribute not set description: {\displaystyle |n_{\alpha }\rangle ={\frac {1}{\sqrt {n_{\alpha }!}}}(b_{\alpha }^{\dagger })^{n_{\alpha }}|0_{\alpha }\rangle .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bc1661c18f3e03b54e4c2256b149e4ca1480caab height: height attribute not set width: width attribute not set description: {\displaystyle b_{\alpha }|n_{\alpha }\rangle ={\frac {1}{\sqrt {n_{\alpha }}}}\psi _{\alpha }\oslash _{+}\psi _{\alpha }^{\otimes n_{\alpha }}={\sqrt {n_{\alpha }}}\psi _{\alpha }^{\otimes (n_{\alpha }-1)}={\sqrt {n_{\alpha }}}|n_{\alpha }-1\rangle .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ef36b45f1a2f5ee79ae90efb795abb4559c3b368 height: height attribute not set width: width attribute not set description: {\displaystyle b_{\alpha }|0_{\alpha }\rangle =0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ca66671c6354c6f9e390bf65ee5fde04944e3ad9 height: height attribute not set width: width attribute not set description: {\displaystyle b_{\alpha }^{\dagger }b_{\alpha }|n_{\alpha }\rangle =n_{\alpha }|n_{\alpha }\rangle ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4f5ca12a24bba24f3d977010400ee2e0febf2ef2 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {n}}_{\alpha }=b_{\alpha }^{\dagger }b_{\alpha }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6937d15f4cad1d93ae3be24678003e212ed78054 height: height attribute not set width: width attribute not set description: {\displaystyle b_{\alpha }^{\dagger }|\cdots ,n_{\beta },n_{\alpha },n_{\gamma },\cdots \rangle ={\sqrt {n_{\alpha }+1}}|\cdots ,n_{\beta },n_{\alpha }+1,n_{\gamma },\cdots \rangle .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6aea491fb6b7c1175f36635583729d3314426788 height: height attribute not set width: width attribute not set description: {\displaystyle b_{\alpha }|\cdots ,n_{\beta },n_{\alpha },n_{\gamma },\cdots \rangle ={\sqrt {n_{\alpha }}}|\cdots ,n_{\beta },n_{\alpha }-1,n_{\gamma },\cdots \rangle .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a5b2c3d6f35ccd6c64d48b10db034a89b3f90a08 height: height attribute not set width: width attribute not set description: {\displaystyle [b_{\alpha }^{\dagger },b_{\beta }^{\dagger }]=[b_{\alpha },b_{\beta }]=0,\quad [b_{\alpha },b_{\beta }^{\dagger }]=\delta _{\alpha \beta }.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/73b3ac1f0c71edb4ff71040f9c2d203c8f4a5914 height: height attribute not set width: width attribute not set description: {\displaystyle x_{\alpha }=(b_{\alpha }+b_{\alpha }^{\dagger })/{\sqrt {2}},\quad p_{\alpha }=(b_{\alpha }-b_{\alpha }^{\dagger })/({\sqrt {2}}\mathrm {i} ),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5f56ce258c75510831a8a14f3e2970ef0a1467 height: height attribute not set width: width attribute not set description: {\displaystyle \hbar =1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/58581c5d5b15030d6075e7fce226e9bd9e239d3a height: height attribute not set width: width attribute not set description: {\displaystyle [x_{\alpha },p_{\beta }]=\mathrm {i} \delta _{\alpha \beta },\quad [x_{\alpha },x_{\beta }]=[p_{\alpha },p_{\beta }]=0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ca31fed66582965ee59d912172fd3b9d260792b2 height: height attribute not set width: width attribute not set description: {\displaystyle c_{\alpha }^{\dagger }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6dcb7aadbcfa0ea1be48b6d5e135843344acbc3c height: height attribute not set width: width attribute not set description: {\displaystyle c_{\alpha }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9e5475c84d2b35c8cb1e9a17a73cabc405ed1f5b height: height attribute not set width: width attribute not set description: {\displaystyle c_{\alpha }^{\dagger }\psi ={\frac {1}{\sqrt {n+1}}}\psi _{\alpha }\otimes _{-}\psi ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/07084597179747c7feda70c8e14004a4fe443054 height: height attribute not set width: width attribute not set description: {\displaystyle c_{\alpha }\psi ={\frac {1}{\sqrt {n}}}\psi _{\alpha }\oslash _{-}\psi ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/de3884d684914a255afcf0be256efb04733a2ec2 height: height attribute not set width: width attribute not set description: {\displaystyle \psi _{\alpha }\otimes _{-}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/768203ef9c808f50c88c02a357dd019ee0e5cb78 height: height attribute not set width: width attribute not set description: {\displaystyle \psi _{\alpha }\oslash _{-}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4688b1db2a73068cde3016e0d2940525beb986c3 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{rl}c_{1}^{\dagger }|1_{1},1_{2}\rangle =&{\frac {1}{\sqrt {2}}}(c_{1}^{\dagger }\psi _{1}\psi _{2}-c_{1}^{\dagger }\psi _{2}\psi _{1})\\=&{\frac {1}{\sqrt {2}}}\left({\frac {1}{\sqrt {3}}}\psi _{1}\otimes _{-}\psi _{1}\psi _{2}-{\frac {1}{\sqrt {3}}}\psi _{1}\otimes _{-}\psi _{2}\psi _{1}\right)\\=&{\frac {1}{\sqrt {2}}}\left({\frac {1}{\sqrt {3}}}(\psi _{1}\psi _{1}\psi _{2}-\psi _{1}\psi _{1}\psi _{2}+\psi _{1}\psi _{2}\psi _{1})-{\frac {1}{\sqrt {3}}}(\psi _{1}\psi _{2}\psi _{1}-\psi _{2}\psi _{1}\psi _{1}+\psi _{2}\psi _{1}\psi _{1})\right)\\=&0.\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/88d25236dbca7f23f32cfd6b5a698e8ae094a615 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{rl}c_{2}|1_{1},1_{2}\rangle =&{\frac {1}{\sqrt {2}}}(c_{2}\psi _{1}\psi _{2}-c_{2}\psi _{2}\psi _{1})\\=&{\frac {1}{\sqrt {2}}}\left({\frac {1}{\sqrt {2}}}\psi _{2}\oslash _{-}\psi _{1}\psi _{2}-{\frac {1}{\sqrt {2}}}\psi _{2}\oslash _{-}\psi _{2}\psi _{1}\right)\\=&{\frac {1}{\sqrt {2}}}\left({\frac {1}{\sqrt {2}}}(0-\psi _{1})-{\frac {1}{\sqrt {2}}}(\psi _{1}-0)\right)\\=&-\psi _{1}\\=&-|1_{1},0_{2}\rangle .\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e6cf7fa9273d7d81ecf1c84f034e330641edba85 height: height attribute not set width: width attribute not set description: {\displaystyle c_{\alpha }^{\dagger }|0_{\alpha }\rangle =\psi _{\alpha }\otimes _{-}1=\psi _{\alpha }=|1_{\alpha }\rangle ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/38d6176ba5d59796a0dc7f165af9e598e2ee6a90 height: height attribute not set width: width attribute not set description: {\displaystyle c_{\alpha }^{\dagger }|1_{\alpha }\rangle ={\frac {1}{\sqrt {2}}}\psi _{\alpha }\otimes _{-}\psi _{\alpha }=0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d3cac8e967d8b103696c4cdcb77e16e0bf0d0c51 height: height attribute not set width: width attribute not set description: {\displaystyle c_{\alpha }|1_{\alpha }\rangle =\psi _{\alpha }\oslash _{-}\psi _{\alpha }=1=|0_{\alpha }\rangle ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c52625e805de5febad84c641f675681084621fbe height: height attribute not set width: width attribute not set description: {\displaystyle c_{\alpha }|0_{\alpha }\rangle =0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/171a7fcd9a924565730087cff85d5fc5fe7cff0b height: height attribute not set width: width attribute not set description: {\displaystyle |n_{\alpha }\rangle =(c_{\alpha }^{\dagger })^{n_{\alpha }}|0_{\alpha }\rangle .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d0783be1bb3f1ce6954c20effb364b6b6e364a8b height: height attribute not set width: width attribute not set description: {\displaystyle c_{\alpha }^{\dagger }c_{\alpha }|n_{\alpha }\rangle =n_{\alpha }|n_{\alpha }\rangle ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/aeb1959a05a14a98995702933198f81688de7c3c height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {n}}_{\alpha }=c_{\alpha }^{\dagger }c_{\alpha }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d4e9ca84b37d6d33d89935613628b17b0cc8b450 height: height attribute not set width: width attribute not set description: {\displaystyle c_{\alpha }^{\dagger }|\cdots ,n_{\beta },n_{\alpha },n_{\gamma },\cdots \rangle =(-1)^{\sum _{\beta <\alpha }n_{\beta }}{\sqrt {1-n_{\alpha }}}|\cdots ,n_{\beta },1+n_{\alpha },n_{\gamma },\cdots \rangle .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/89ae2ebf305348e9ebbf52486cbb09b7bb4e142a height: height attribute not set width: width attribute not set description: {\displaystyle c_{\alpha }|\cdots ,n_{\beta },n_{\alpha },n_{\gamma },\cdots \rangle =(-1)^{\sum _{\beta <\alpha }n_{\beta }}{\sqrt {n_{\alpha }}}|\cdots ,n_{\beta },1-n_{\alpha },n_{\gamma },\cdots \rangle .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4431a584dc95011778d7983c1de3e048e8efa39b height: height attribute not set width: width attribute not set description: {\displaystyle (-1)^{\sum _{\beta <\alpha }n_{\beta }}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/af4f50a8d2b62073e7c819f8e1fe5f264da2ab21 height: height attribute not set width: width attribute not set description: {\displaystyle \{c_{\alpha }^{\dagger },c_{\beta }^{\dagger }\}=\{c_{\alpha },c_{\beta }\}=0,\quad \{c_{\alpha },c_{\beta }^{\dagger }\}=\delta _{\alpha \beta }.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/102023294be22cff49653a6a384f26e2ca05de5e height: height attribute not set width: width attribute not set description: {\displaystyle c_{\alpha }\neq c_{\alpha }^{\dagger }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f09d11d657fdcebd8cb31365335c7d7566f50018 height: height attribute not set width: width attribute not set description: {\displaystyle \chi _{\alpha ,{\text{re}}}=(c_{\alpha }+c_{\alpha }^{\dagger })/{\sqrt {2}},\quad \chi _{\alpha ,{\text{im}}}=(c_{\alpha }-c_{\alpha }^{\dagger })/({\sqrt {2}}\mathrm {i} ),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/31fb27cacf1216252f93c585ca17fd87b7d61d68 height: height attribute not set width: width attribute not set description: {\displaystyle \{\chi _{i},\chi _{j}\}=\delta _{ij},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f4cbf8bbc622154cda8208d6e339495fe16a1f9a height: height attribute not set width: width attribute not set description: {\displaystyle i,j} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0c734f2c06f98dfef798942d05f04acf1292d0b1 height: height attribute not set width: width attribute not set description: {\displaystyle a_{\nu }^{\dagger }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468 height: height attribute not set width: width attribute not set description: {\displaystyle \nu } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/26c0c88a2a63aa2ba345f9ac4acb1e27218a4d04 height: height attribute not set width: width attribute not set description: {\displaystyle (c_{\nu }^{\dagger })} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4a257485e8e2c3d8a8b9e00e44677d9e26452713 height: height attribute not set width: width attribute not set description: {\displaystyle (b_{\nu }^{\dagger })} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e478d6f260286a13b6516ffecb4787fb0b2aaae5 height: height attribute not set width: width attribute not set description: {\displaystyle \psi (\mathbf {r} )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4dd9f5ead305297426c991a45eb86338418f46b7 height: height attribute not set width: width attribute not set description: {\displaystyle \psi ^{\dagger }(\mathbf {r} )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f4f008dbf5817545bca49bb6f7fa47e16203bd7d height: height attribute not set width: width attribute not set description: {\displaystyle \psi (\mathbf {r} )=\sum _{\nu }\psi _{\nu }\left(\mathbf {r} \right)a_{\nu }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/55285f64c56d5ff436b91525afe6db710d92dc1a height: height attribute not set width: width attribute not set description: {\displaystyle \psi ^{\dagger }(\mathbf {r} )=\sum _{\nu }\psi _{\nu }^{*}\left(\mathbf {r} \right)a_{\nu }^{\dagger }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/120cd5ab34898cf69a2109e991de3bb411cd0639 height: height attribute not set width: width attribute not set description: {\displaystyle \psi _{\nu }\left(\mathbf {r} \right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7749212bdc05910415d253f79a8f24502662ca0d height: height attribute not set width: width attribute not set description: {\displaystyle \psi _{\nu }^{*}\left(\mathbf {r} \right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/adfab9b2bae3d90b9a2aaacecf82f9882e3c4eca height: height attribute not set width: width attribute not set description: {\displaystyle \left[\psi (\mathbf {r} _{1}),\psi ^{\dagger }(\mathbf {r} _{2})\right]=\delta (\mathbf {r} _{1}-\mathbf {r} _{2})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dfc012cdc1a87642b4e6e67dae64ce85476c997d height: height attribute not set width: width attribute not set description: {\displaystyle \{\psi (\mathbf {r} _{1}),\psi ^{\dagger }(\mathbf {r} _{2})\}=\delta (\mathbf {r} _{1}-\mathbf {r} _{2})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f6d1424faf283a53b7dd180ace9c8e8e40521633 height: height attribute not set width: width attribute not set description: {\displaystyle \psi (\mathbf {r} )={1 \over {\sqrt {v}}}\sum _{\mathbf {k} }e^{i\mathbf {k\cdot r} }a_{\mathbf {k} }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c082dcc7018ec0de340941253e12e583a2655f13 height: height attribute not set width: width attribute not set description: {\displaystyle \psi ^{\dagger }(\mathbf {r} )={1 \over {\sqrt {v}}}\sum _{\mathbf {k} }e^{-i\mathbf {k\cdot r} }a_{\mathbf {k} }^{\dagger }} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/0/0b/wikiversity_logo_2017.svg/40px-wikiversity_logo_2017.svg.png height: 33 width: 40 description: no alt description found |
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