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Display information for equation id:math.349.5 on revision:349

* Page found: Liouville-von-Neumann-Gleichung (eq math.349.5)

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Hash: 4b3c16f9532daa71144214e2be27557e

TeX (original user input):

\begin{align}
  & \left\langle  \mathfrak{i}{{\partial }_{t}}\Psi \left( t \right) \right|=\left\langle  \hat{H}\Psi \left( t \right) \right| \\
 & \text{-}\mathfrak{i}{{\partial }_{t}}\left\langle  \Psi \left( t \right) \right|=\left\langle  \Psi \left( t \right) \right|\hat{H},\,\left( \hat{H}={{{\hat{H}}}^{+}} \right)\Rightarrow {{\partial }_{t}}\left\langle  \Psi \left( t \right) \right|=\mathfrak{i}\left\langle  \Psi \left( t \right) \right|\hat{H} \\
\end{align}

TeX (checked):

{\begin{aligned}&\left\langle {\mathfrak {i}}{{\partial }_{t}}\Psi \left(t\right)\right|=\left\langle {\hat {H}}\Psi \left(t\right)\right|\\&{\text{-}}{\mathfrak {i}}{{\partial }_{t}}\left\langle \Psi \left(t\right)\right|=\left\langle \Psi \left(t\right)\right|{\hat {H}},\,\left({\hat {H}}={{\hat {H}}^{+}}\right)\Rightarrow {{\partial }_{t}}\left\langle \Psi \left(t\right)\right|={\mathfrak {i}}\left\langle \Psi \left(t\right)\right|{\hat {H}}\\\end{aligned}}

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𝔦tΨ(t)|=ĤΨ(t)|-𝔦tΨ(t)|=Ψ(t)|Ĥ,(Ĥ=Ĥ+)tΨ(t)|=𝔦Ψ(t)|Ĥ
<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><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></mrow><msub><mi></mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mi>Ψ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><mover><mi>H</mi><mo stretchy="false">̂</mo></mover><mi>Ψ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="ORD"><mtext>-</mtext></mrow><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></mrow><msub><mi></mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><mi>Ψ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><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><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mover><mi>H</mi><mo stretchy="false">̂</mo></mover><mo>,</mo><mspace width="0.167em"></mspace><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>H</mi><mo stretchy="false">̂</mo></mover><mo stretchy="false">=</mo><msup><mover><mi>H</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false"></mo><msub><mi></mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><mi>Ψ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><mi>Ψ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mover><mi>H</mi><mo stretchy="false">̂</mo></mover></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Identifiers

  • 𝔦
  • t
  • Ψ
  • t
  • Ĥ
  • Ψ
  • t
  • 𝔦
  • t
  • Ψ
  • t
  • Ψ
  • t
  • Ĥ
  • Ĥ
  • Ĥ
  • t
  • Ψ
  • t
  • 𝔦
  • Ψ
  • t
  • Ĥ

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