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Display information for equation id:math.2405.32 on revision:2405
* Page found: Quantenmechanische Gleichgewichtsverteilungen (eq math.2405.32)
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Hash: dace5f8332cdc26c89034ca8fdbe90d3
TeX (original user input):
\begin{align}
& tr\hat{X}:=\sum\limits_{\alpha }^{{}}{{}}\left\langle \alpha \right|\hat{X}\left| \alpha \right\rangle =\sum\limits_{\alpha ,\beta ,\beta \acute{\ }}^{{}}{{}}\left\langle \alpha | \beta \right\rangle \left\langle \beta \right|\hat{X}\left| \beta \acute{\ } \right\rangle \left\langle \beta \acute{\ } | \alpha \right\rangle =\sum\limits_{\beta ,\beta }^{{}}{{}}\left\langle \beta \right|\hat{X}\left| \beta \acute{\ } \right\rangle \sum\limits_{\alpha }^{{}}{{}}\left\langle \beta \acute{\ } | \alpha \right\rangle \left\langle \alpha | \beta \right\rangle \\
& \sum\limits_{\alpha }^{{}}{{}}\left\langle \beta \acute{\ } | \alpha \right\rangle \left\langle \alpha | \beta \right\rangle =\left\langle \beta \acute{\ } | \beta \right\rangle ={{\delta }_{\beta \acute{\ }\beta }} \\
& tr\hat{X}=\sum\limits_{\beta }^{{}}{{}}\left\langle \beta \right|\hat{X}\left| \beta \right\rangle \\
\end{align}
TeX (checked):
{\begin{aligned}&tr{\hat {X}}:=\sum \limits _{\alpha }^{}{}\left\langle \alpha \right|{\hat {X}}\left|\alpha \right\rangle =\sum \limits _{\alpha ,\beta ,\beta {\acute {\ }}}^{}{}\left\langle \alpha |\beta \right\rangle \left\langle \beta \right|{\hat {X}}\left|\beta {\acute {\ }}\right\rangle \left\langle \beta {\acute {\ }}|\alpha \right\rangle =\sum \limits _{\beta ,\beta }^{}{}\left\langle \beta \right|{\hat {X}}\left|\beta {\acute {\ }}\right\rangle \sum \limits _{\alpha }^{}{}\left\langle \beta {\acute {\ }}|\alpha \right\rangle \left\langle \alpha |\beta \right\rangle \\&\sum \limits _{\alpha }^{}{}\left\langle \beta {\acute {\ }}|\alpha \right\rangle \left\langle \alpha |\beta \right\rangle =\left\langle \beta {\acute {\ }}|\beta \right\rangle ={{\delta }_{\beta {\acute {\ }}\beta }}\\&tr{\hat {X}}=\sum \limits _{\beta }^{}{}\left\langle \beta \right|{\hat {X}}\left|\beta \right\rangle \\\end{aligned}}
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