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Display information for equation id:math.2402.30 on revision:2402

* Page found: Quantenmechanische Gleichgewichtsverteilungen (eq math.2402.30)

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Hash: 748ad6e03378774aad061bb4d54bd63a

TeX (original user input): 

\begin{align}
& \left\langle {\hat{M}} \right\rangle =\left\langle  \Psi  \right|\hat{M}\left| \Psi  \right\rangle =\sum\limits_{\alpha }^{{}}{{}}\left\langle  \alpha  \right|\left| \Psi  \right\rangle \left\langle  \Psi  \right|\hat{M}\left| \alpha  \right\rangle =\sum\limits_{\alpha }^{{}}{{}}\left\langle  \alpha  \right|{{{\hat{P}}}_{\Psi }}\hat{M}\left| \alpha  \right\rangle :=tr\left( {{{\hat{P}}}_{\Psi }}\hat{M} \right)=tr\left( \hat{M}{{{\hat{P}}}_{\Psi }} \right) \\
& tr\hat{X}:=\sum\limits_{\alpha }^{{}}{{}}\left\langle  \alpha  \right|\hat{X}\left| \alpha  \right\rangle  \\
\end{align}

TeX (checked): 

{\begin{aligned}&\left\langle {\hat {M}}\right\rangle =\left\langle \Psi \right|{\hat {M}}\left|\Psi \right\rangle =\sum \limits _{\alpha }^{}{}\left\langle \alpha \right|\left|\Psi \right\rangle \left\langle \Psi \right|{\hat {M}}\left|\alpha \right\rangle =\sum \limits _{\alpha }^{}{}\left\langle \alpha \right|{{\hat {P}}_{\Psi }}{\hat {M}}\left|\alpha \right\rangle :=tr\left({{\hat {P}}_{\Psi }}{\hat {M}}\right)=tr\left({\hat {M}}{{\hat {P}}_{\Psi }}\right)\\&tr{\hat {X}}:=\sum \limits _{\alpha }^{}{}\left\langle \alpha \right|{\hat {X}}\left|\alpha \right\rangle \\\end{aligned}}

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⟨M̂⟩=⟨Ψ|M̂|Ψ⟩=∑α⟨α||Ψ⟩⟨Ψ|M̂|α⟩=∑α⟨α|P̂ΨM̂|α⟩:=tr(P̂ΨM̂)=tr(M̂P̂Ψ)trX̂:=∑α⟨α|X̂|α⟩
<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mover><mi>M</mi><mo stretchy="false">̂</mo></mover><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>Ψ</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mover><mi>M</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>Ψ</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><munderover><mo form="prefix" movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>α</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>Ψ</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>Ψ</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mover><mi>M</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>α</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><munderover><mo form="prefix" movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>α</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mover><mi>P</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>Ψ</mi></mrow></msub><mover><mi>M</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>α</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">:=</mo><mi>t</mi><mi>r</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mover><mi>P</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>Ψ</mi></mrow></msub><mover><mi>M</mi><mo stretchy="false">̂</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mi>t</mi><mi>r</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>M</mi><mo stretchy="false">̂</mo></mover><msub><mover><mi>P</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>Ψ</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>t</mi><mi>r</mi><mover><mi>X</mi><mo stretchy="false">̂</mo></mover><mo stretchy="false">:=</mo><munderover><mo form="prefix" movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>α</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mover><mi>X</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>α</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Quantenmechanische Gleichgewichtsverteilungen page

Identifiers

  • M̂
  • Ψ
  • M̂
  • Ψ
  • α
  • α
  • Ψ
  • Ψ
  • M̂
  • α
  • α
  • α
  • P̂Ψ
  • M̂
  • α
  • t
  • r
  • P̂Ψ
  • M̂
  • t
  • r
  • M̂
  • P̂Ψ
  • t
  • r
  • X̂
  • α
  • α
  • X̂
  • α

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