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Display information for equation id:math.1649.11 on revision:1649

* Page found: Dynamik im Schrödinger- Heisenberg- und Wechselwirkungsbild (eq math.1649.11)

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Dynamik im Schrödinger- Heisenberg- und Wechselwirkungsbild Eq: math.1649.11

Hash: 34cc83e8666eabc1445538d907463da4

TeX (original user input):

\begin{align}
& \frac{d}{dt}\left\langle {\hat{F}} \right\rangle =\frac{d}{dt}{{\left\langle  \Psi  \right|}_{t}}\hat{F}{{\left| \Psi  \right\rangle }_{t}}={{\left\langle  \Psi  \right|}_{t}}\frac{\partial \hat{F}}{\partial t}{{\left| \Psi  \right\rangle }_{t}}+\left( \frac{\partial }{\partial t}{{\left\langle  \Psi  \right|}_{t}} \right)\frac{d}{dt}\hat{F}{{\left| \Psi  \right\rangle }_{t}}+{{\left\langle  \Psi  \right|}_{t}}\hat{F}\left( \frac{\partial }{\partial t}{{\left| \Psi  \right\rangle }_{t}} \right) \\
& \left( \frac{\partial }{\partial t}{{\left\langle  \Psi  \right|}_{t}} \right)=-\frac{1}{i\hbar }{{\left\langle  \Psi  \right|}_{t}}\hat{H} \\
& \frac{\partial }{\partial t}{{\left| \Psi  \right\rangle }_{t}}=\frac{1}{i\hbar }\hat{H}{{\left| \Psi  \right\rangle }_{t}} \\
\end{align}

TeX (checked):

{\begin{aligned}&{\frac {d}{dt}}\left\langle {\hat {F}}\right\rangle ={\frac {d}{dt}}{{\left\langle \Psi \right|}_{t}}{\hat {F}}{{\left|\Psi \right\rangle }_{t}}={{\left\langle \Psi \right|}_{t}}{\frac {\partial {\hat {F}}}{\partial t}}{{\left|\Psi \right\rangle }_{t}}+\left({\frac {\partial }{\partial t}}{{\left\langle \Psi \right|}_{t}}\right){\frac {d}{dt}}{\hat {F}}{{\left|\Psi \right\rangle }_{t}}+{{\left\langle \Psi \right|}_{t}}{\hat {F}}\left({\frac {\partial }{\partial t}}{{\left|\Psi \right\rangle }_{t}}\right)\\&\left({\frac {\partial }{\partial t}}{{\left\langle \Psi \right|}_{t}}\right)=-{\frac {1}{i\hbar }}{{\left\langle \Psi \right|}_{t}}{\hat {H}}\\&{\frac {\partial }{\partial t}}{{\left|\Psi \right\rangle }_{t}}={\frac {1}{i\hbar }}{\hat {H}}{{\left|\Psi \right\rangle }_{t}}\\\end{aligned}}

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\begin{aligned} \frac{d}{d t} ⟨ \hat{F} ⟩ = \frac{d}{d t} {⟨ Ψ |}_{t} \hat{F} {| Ψ ⟩}_{t} = {⟨ Ψ |}_{t} \frac{\partial \hat{F}}{\partial t} {| Ψ ⟩}_{t} + (\frac{\partial}{\partial t} {⟨ Ψ |}_{t}) \frac{d}{d t} \hat{F} {| Ψ ⟩}_{t} + {⟨ Ψ |}_{t} \hat{F} (\frac{\partial}{\partial t} {| Ψ ⟩}_{t}) \\ (\frac{\partial}{\partial t} {⟨ Ψ |}_{t}) = - \frac{1}{i ℏ} {⟨ Ψ |}_{t} \hat{H} \\ \frac{\partial}{\partial t} {| Ψ ⟩}_{t} = \frac{1}{i ℏ} \hat{H} {| Ψ ⟩}_{t} \end{aligned}

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Translations to Computer Algebra Systems

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Identifiers

$d$

$d$

$t$

$\hat{F}$

$d$

$d$

$t$

$Ψ_{t}$

$\hat{F}$

$Ψ_{t}$

$Ψ_{t}$

$\hat{F}$

$t$

$Ψ_{t}$

$t$

$Ψ_{t}$

$d$

$d$

$t$

$\hat{F}$

$Ψ_{t}$

$Ψ_{t}$

$\hat{F}$

$t$

$Ψ_{t}$

$t$

$Ψ_{t}$

$i$

$Ψ_{t}$

$\hat{H}$

$t$

$Ψ_{t}$

$i$

$\hat{H}$

$Ψ_{t}$

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