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Display information for equation id:math.2410.48 on revision:2410
* Page found: Quantenmechanische Gleichgewichtsverteilungen (eq math.2410.48)
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Hash: 1c5c732a5a7d37e6fa2a56d250c813ef
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 | \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 |\beta \right\rangle =\sum \limits _{\beta }^{}{}{{P}_{\beta }}\left\langle \beta \right|{\hat {M}}\left|\beta \right\rangle
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MathML (2.198 KB / 378 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>M</mi><mo>^</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><mi>t</mi><mi>r</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>M</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ρ</mi><mo>^</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>α</mi><mo>,</mo><mi>β</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>β</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>M</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>α</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>α</mi><mo>|</mo><mi>β</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>β</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>M</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>β</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mstyle></mrow></math>
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