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Display information for equation id:math.2718.7 on revision:2718

* Page found: Fermis Goldene Regel (eq math.2718.7)

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Hash: 9448ae21b4f3992dd62d74cffbb8f281

TeX (original user input):

\begin{align}
  & \frac{d}{dt}{{\left| \Psi \left( t \right) \right\rangle }_{I}}=\text{i}{{H}_{0}}{{\left| \Psi \left( t \right) \right\rangle }_{I}}-\text{i}U_{0}^{+}\left( {{H}_{0}}+V\left( t \right) \right)\left| \Psi \left( t \right) \right\rangle  \\ 
 & =\text{i}\left( {{H}_{0}}-U_{0}^{+}\left( {{H}_{0}}+V\left( t \right) \right){{U}_{0}} \right){{\left| \Psi \left( t \right) \right\rangle }_{I}}  
\end{align}

TeX (checked):

{\begin{aligned}&{\frac {d}{dt}}{{\left|\Psi \left(t\right)\right\rangle }_{I}}={\text{i}}{{H}_{0}}{{\left|\Psi \left(t\right)\right\rangle }_{I}}-{\text{i}}U_{0}^{+}\left({{H}_{0}}+V\left(t\right)\right)\left|\Psi \left(t\right)\right\rangle \\&={\text{i}}\left({{H}_{0}}-U_{0}^{+}\left({{H}_{0}}+V\left(t\right)\right){{U}_{0}}\right){{\left|\Psi \left(t\right)\right\rangle }_{I}}\end{aligned}}

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MathML (3.281 KB / 458 B) :

ddt|Ψ(t)I=iH0|Ψ(t)IiU0+(H0+V(t))|Ψ(t)=i(H0U0+(H0+V(t))U0)|Ψ(t)I
<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="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi mathvariant="normal">&#x03A8;</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">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mi>I</mi></mrow></msub><mo>=</mo><mrow data-mjx-texclass="ORD"><mtext>i</mtext></mrow><msub><mi>H</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi mathvariant="normal">&#x03A8;</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">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mi>I</mi></mrow></msub><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mtext>i</mtext></mrow><msubsup><mi>U</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>H</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><mi>V</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><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi mathvariant="normal">&#x03A8;</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">&#x27E9;</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mrow data-mjx-texclass="ORD"><mtext>i</mtext></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>H</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>&#x2212;</mo><msubsup><mi>U</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>H</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><mi>V</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><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi mathvariant="normal">&#x03A8;</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">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mi>I</mi></mrow></msub></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Identifiers

  • d
  • d
  • t
  • Ψ
  • t
  • I
  • H0
  • Ψ
  • t
  • I
  • U
  • H0
  • V
  • t
  • Ψ
  • t
  • H0
  • U
  • H0
  • V
  • t
  • U0
  • Ψ
  • t
  • I

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