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SEO Keyword summary for en.wikipedia.org/wiki/mathematical_formulations_of_quantum_mechanics
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 quantum
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Short Tail Keywords quantum mechanics displaystyle |
long Tail Keywords (2 words) quantum mechanics quantum theory hilbert space psi rangle time evolution |
long Tail Keywords (3 words) quantum field theory displaystyle psi rangle foundations of quantum postulates of quantum old quantum theory formulation of quantum irangle langle psi |
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mathematical formulation quantum mechanics wikipedia
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wikipedia free encyclopedia displaystyle ihbar frac ddtpsi rangle hat hpsi light right frequency psi mathcal rho sum kpkrho kotimes kpk textstyle otimes langle apsi alpha beginalignedmathbb anlangle anpsi textdiscrete nondegenerate spectrummathbb ansum ignlangle anipsi degenerate spectrumdmathbb dalpha textcontinuous spectrumendaligned operatorname arho mathbb anoperatorname anrangle anrho dots anmrangle pnan anm pnrho quad overset anlongrightarrow pnpsi sqrt pndagger trangle htpsi utt tutt udagger sigma shbar hbar pbigg cdots phi bigg equiv pcdots ninjcdots srangle arangle mathbf isigma idots jsigma jdots scdot nnax ldots xnfrac nleftbeginmatrixpsi xnpsi xnvdots vdots ddots nnx nnxnendmatrixright xnsrangle prod jnjnsum pleftxp rightrangle leftxp leftxpnrightrangle ddtleftpsi trightrangle hleftpsi leftpsi tsrightrangle utleftpsi srightrangle uteihbar utmathcal tleftexp leftfrac int tdthtrightright cdot bntn bintin geq tin atutaut mid atmid tmid amid ddtatfrac hatfrac partial atpartial hrm inttleftpsi ddtatath inttequiv eihbar veihbar strangle eihrm sthbar itrangle eih mathrm thbar arm hteihrm seihrm iteih seih steihrm steih aint lambda doperatorname alambda abpsi irangle imid fifi ipsi fipsi wikimedia foundation powered mediawiki
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mathematical formulations of quantum mechanics
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wiki quantum mechanics
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https://wikimedia.org/api/rest_v1/media/math/render/svg/998ad382ec46921e1281154a441747adf1997b9e height: height attribute not set width: width attribute not set description: {\displaystyle \psi (\dots ,\,\mathbf {r} _{i},\sigma _{i},\,\dots ,\,\mathbf {r} _{j},\sigma _{j},\,\dots )=(-1)^{2s}\cdot \psi (\dots ,\,\mathbf {r} _{j},\sigma _{j},\,\dots ,\mathbf {r} _{i},\sigma _{i},\,\dots )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c3aed21bd5caf4c26f6223a4217d75aa86330f43 height: height attribute not set width: width attribute not set description: {\displaystyle \psi _{n_{1}\cdots n_{n}}^{(a)}(x_{1},\ldots ,x_{n})={\frac {1}{\sqrt {n!}}}\left|{\begin{matrix}\psi _{n_{1}}(x_{1})&\psi _{n_{1}}(x_{2})&\cdots &\psi _{n_{1}}(x_{n})\\\psi _{n_{2}}(x_{1})&\psi _{n_{2}}(x_{2})&\cdots &\psi _{n_{2}}(x_{n})\\\vdots &\vdots &\ddots &\vdots \\\psi _{n_{n}}(x_{1})&\psi _{n_{n}}(x_{2})&\cdots &\psi _{n_{n}}(x_{n})\\\end{matrix}}\right|} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/58476bba63e99495e69aeea4efe81d4b7f84e470 height: height attribute not set width: width attribute not set description: {\displaystyle |x_{1}x_{2}\cdots x_{n};s\rangle ={\frac {\prod _{j}n_{j}!}{n!}}\sum _{p}\left|x_{p(1)}\right\rangle \left|x_{p(2)}\right\rangle \cdots \left|x_{p(n)}\right\rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d2c97b31dca4eeefe57123a12e69e6ea73f3dcd2 height: height attribute not set width: width attribute not set description: {\displaystyle n_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f3b692255e8d80417f422629cb61362d7dbc9b64 height: height attribute not set width: width attribute not set description: {\displaystyle i\hbar {\frac {d}{dt}}\left|\psi (t)\right\rangle =h\left|\psi (t)\right\rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e56df7a8a0e743e7f5ffde2916f0d80cfbffafbe height: height attribute not set width: width attribute not set description: {\displaystyle \left|\psi (t+s)\right\rangle =u(t)\left|\psi (s)\right\rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3d7034b4e9543aebae32482a5fe6a607ce47c4a8 height: height attribute not set width: width attribute not set description: {\displaystyle u(t)=e^{-(i/\hbar )th}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/442eb5c646ec193e2cc7e5056896a8648396079b height: height attribute not set width: width attribute not set description: {\displaystyle u(t)={\mathcal {t}}\left[\exp \left(-{\frac {i}{\hbar }}\int _{t_{0}}^{t}dt'\,h(t')\right)\right],} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8236d074e42310f5dc24d1d2b5b8f5981c3e87ba height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {t}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/838f98fb88bd073c9595c749b0b82099fc7f8437 height: height attribute not set width: width attribute not set description: {\displaystyle b_{1}(t_{1})\cdot b_{2}(t_{2})\cdot \dots \cdot b_{n}(t_{n})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7f7b4818a96164af9f340022bc5bd2709321bee9 height: height attribute not set width: width attribute not set description: {\displaystyle b_{i_{1}}(t_{i_{1}})\cdot b_{i_{2}}(t_{i_{2}})\cdot \dots \cdot b_{i_{n}}(t_{i_{n}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3650a56b252693b70247bdbf4248034bdae5a4fc height: height attribute not set width: width attribute not set description: {\displaystyle t_{i_{1}}\geq t_{i_{2}}\geq \dots \geq t_{i_{n}}\,.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d23b83fe688e0cdb40e8ffba01a2f0f0488b804c height: height attribute not set width: width attribute not set description: {\displaystyle \left|\psi \right\rangle =\left|\psi (0)\right\rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5afc0a80548c87e308a4ae27fef667a822813a14 height: height attribute not set width: width attribute not set description: {\displaystyle a(t)=u(-t)au(t).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0b8c0e9169ab1c57391f6480d49ace5bcb36a32d height: height attribute not set width: width attribute not set description: {\displaystyle \langle \psi \mid a(t)\mid \psi \rangle =\langle \psi (t)\mid a\mid \psi (t)\rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7d714d59756ef17027e03f666547917ba07d8057 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {d}{dt}}a(t)={\frac {i}{\hbar }}[h,a(t)]+{\frac {\partial a(t)}{\partial t}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/540045c7e87fab9ef7dd5996d8388f88cd36cb6d height: height attribute not set width: width attribute not set description: {\displaystyle i\hbar {\frac {d}{dt}}\left|\psi (t)\right\rangle ={h}_{\rm {int}}(t)\left|\psi (t)\right\rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1fe8dccc41b7f0b775dcb47dde6daca9ae2f080a height: height attribute not set width: width attribute not set description: {\displaystyle i\hbar {\frac {d}{dt}}a(t)=[a(t),h_{0}].} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/959f447d3d7581eaa714c73e2b9e19e6888477ef height: height attribute not set width: width attribute not set description: {\displaystyle h_{\rm {int}}(t)\equiv e^{{(i/\hbar })th_{0}}\,v\,e^{{(-i/\hbar })th_{0}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6f7e8476598d735d3fa5be6979777f685fb8ea2f height: height attribute not set width: width attribute not set description: {\displaystyle |\psi _{\rm {s}}(t)\rangle =e^{-ih_{\rm {s}}~t/\hbar }|\psi _{\rm {s}}(0)\rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6239a430d0eac4e07abc9f7926d65b12b4755c8c height: height attribute not set width: width attribute not set description: {\displaystyle |\psi _{\rm {i}}(t)\rangle =e^{ih_{0,\mathrm {s} }~t/\hbar }|\psi _{\rm {s}}(t)\rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9fed2a30b52c2506bf999ba176813e78a5cd6f28 height: height attribute not set width: width attribute not set description: {\displaystyle a_{\rm {h}}(t)=e^{ih_{\rm {s}}~t/\hbar }a_{\rm {s}}e^{-ih_{\rm {s}}~t/\hbar }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e17359cb3e0e75ad9db7c54218cb5ddedcb7605e height: height attribute not set width: width attribute not set description: {\displaystyle a_{\rm {i}}(t)=e^{ih_{0,\mathrm {s} }~t/\hbar }a_{\rm {s}}e^{-ih_{0,\mathrm {s} }~t/\hbar }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/238d1dec8256c54d7316d3656ca666eb32784d6e height: height attribute not set width: width attribute not set description: {\displaystyle \rho _{\rm {s}}(t)=e^{-ih_{\rm {s}}~t/\hbar }\rho _{\rm {s}}(0)e^{ih_{\rm {s}}~t/\hbar }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4f578fe89295524333c363ccf0b9781275894c7d height: height attribute not set width: width attribute not set description: {\displaystyle \rho _{\rm {i}}(t)=e^{ih_{0,\mathrm {s} }~t/\hbar }\rho _{\rm {s}}(t)e^{-ih_{0,\mathrm {s} }~t/\hbar }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/72d10f58c0ca5130e744051e21e5b8b9ddb6d587 height: height attribute not set width: width attribute not set description: {\displaystyle a=\int \lambda \,d\operatorname {e} _{a}(\lambda ),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5dc91e39cb8fc76670267ca3c7315d346b46adad height: height attribute not set width: width attribute not set description: {\displaystyle \langle \psi \mid \operatorname {e} _{a}\psi \rangle .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a17e2730e3d187b7a2f3e7f4501a4c67bfb3a9c6 height: height attribute not set width: width attribute not set description: {\displaystyle \operatorname {e} _{a}(b)=|\psi _{i}\rangle \langle \psi _{i}|,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7df757d215e5bfcfd06e6f5733890f61d2d7bca9 height: height attribute not set width: width attribute not set description: {\displaystyle \langle \psi \mid \operatorname {e} _{a}\psi \rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9d448cca751f067300353031820cdb20b114915a height: height attribute not set width: width attribute not set description: {\displaystyle \langle \psi |\psi _{i}\rangle \langle \psi _{i}\mid \psi \rangle =|\langle \psi \mid \psi _{i}\rangle |^{2}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5014b6330cd16bdcd79e204c8b602f26837c464a height: height attribute not set width: width attribute not set description: {\displaystyle |\psi _{i}\rangle \langle \psi _{i}|} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6ea0fd3eaffd19d5905a5ef5b75f82f67a9bb202 height: height attribute not set width: width attribute not set description: {\displaystyle f_{i}f_{i}^{*}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d5fb9ab146b1b34d30a2f23df3c6efeff377b84e height: height attribute not set width: width attribute not set description: {\displaystyle |\psi _{i}\rangle \langle \psi _{i}|\psi \rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/66faab68701ab346299c84389b228fa481841c6b height: height attribute not set width: width attribute not set description: {\displaystyle f_{i}|\psi \rangle .} |
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