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Display information for equation id:math.2402.48 on revision:2402

* Page found: Quantenmechanische Gleichgewichtsverteilungen (eq math.2402.48)

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Hash: f45e1fd272ff29d99775d29a00fd2fd8

TeX (original user input):

\left\langle {\hat{M}} \right\rangle =tr\left( \hat{M}\hat{\rho } \right)=\sum\limits_{\alpha ,\beta }^{{}}{{}}\left\langle  \beta  \right|\hat{M}\left| \alpha  \right\rangle {{P}_{\alpha }}\left\langle  \alpha  \right|\left| \beta  \right\rangle =\sum\limits_{\beta }^{{}}{{}}{{P}_{\beta }}\left\langle  \beta  \right|\hat{M}\left| \beta  \right\rangle

TeX (checked):

\left\langle {\hat {M}}\right\rangle =tr\left({\hat {M}}{\hat {\rho }}\right)=\sum \limits _{\alpha ,\beta }^{}{}\left\langle \beta \right|{\hat {M}}\left|\alpha \right\rangle {{P}_{\alpha }}\left\langle \alpha \right|\left|\beta \right\rangle =\sum \limits _{\beta }^{}{}{{P}_{\beta }}\left\langle \beta \right|{\hat {M}}\left|\beta \right\rangle

LaTeXML (experimental; uses MathML) rendering

MathML (13.032 KB / 1.877 KB) :

{\displaystyle{\displaystyle\left\langle{\hat{M}}\right\rangle=tr\left(\hat{M}% \hat{\rho}\right)=\sum\limits_{\alpha,\beta}{{}}\left\langle\beta\right|\hat{M% }\left|\alpha\right\rangle{{P}_{\alpha}}\left\langle\alpha\right|\left|\beta% \right\rangle=\sum\limits_{\beta}{{}}{{P}_{\beta}}\left\langle\beta\right|\hat% {M}\left|\beta\right\rangle}}

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    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\left\langle{\hat{M}}\right\rangle=tr\left(\hat{M}%
\hat{\rho}\right)=\sum\limits_{\alpha,\beta}{{}}\left\langle\beta\right|\hat{M%
}\left|\alpha\right\rangle{{P}_{\alpha}}\left\langle\alpha\right|\left|\beta%
\right\rangle=\sum\limits_{\beta}{{}}{{P}_{\beta}}\left\langle\beta\right|\hat%
{M}\left|\beta\right\rangle}}</annotation>
  </semantics>
</math>

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⟨ \hat{M} ⟩ = t r (\hat{M} \hat{ρ}) = \sum_{α, β}^{} ⟨ β | \hat{M} | α ⟩ P_{α} ⟨ α | | β ⟩ = \sum_{β}^{} P_{β} ⟨ β | \hat{M} | β ⟩

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$\hat{M}$

$t$

$r$

$\hat{M}$

$\hat{ρ}$

$α$

$β$

$β$

$\hat{M}$

$α$

$P_{α}$

$α$

$β$

$β$

$P_{β}$

$β$

$\hat{M}$

$β$

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