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Display information for equation id:math.2719.7 on revision:2719

* Page found: Fermis Goldene Regel (eq math.2719.7)

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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}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (27.312 KB / 2.975 KB) :

d d ⁢ t ⁢ | Ψ ⁢ ( t ) ⟩ I = i ⁢ H 0 ⁢ | Ψ ⁢ ( t ) ⟩ I - i ⁢ U 0 + ⁢ ( H 0 + V ⁢ ( t ) ) ⁢ | Ψ ⁢ ( t ) ⟩ = i ⁢ ( H 0 - U 0 + ⁢ ( H 0 + V ⁢ ( t ) ) ⁢ U 0 ) ⁢ | Ψ ⁢ ( t ) ⟩ I missing-subexpression 𝑑 𝑑 𝑡 subscript ket Ψ 𝑡 𝐼 i subscript 𝐻 0 subscript ket Ψ 𝑡 𝐼 i superscript subscript 𝑈 0 subscript 𝐻 0 𝑉 𝑡 ket Ψ 𝑡 missing-subexpression absent i subscript 𝐻 0 superscript subscript 𝑈 0 subscript 𝐻 0 𝑉 𝑡 subscript 𝑈 0 subscript ket Ψ 𝑡 𝐼 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\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\\ &\displaystyle=\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)⟩I−iU0+(H0+V(t))|Ψ(t)⟩=i(H0−U0+(H0+V(t))U0)|Ψ(t)⟩I

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Calculated based on the variables occurring on the entire Fermis Goldene Regel page

Identifiers

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Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“