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Display information for equation id:math.1732.19 on revision:1732

* Page found: Zeitabhängige Störungsrechnung (eq math.1732.19)

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Hash: ff2874dfae9f868d1444b0f4186a8085

TeX (original user input):

\begin{align}

& {{c}_{m}}(t){{E}_{m}}+{{e}^{-\left( i\frac{{{E}_{m}}t}{\hbar } \right)}}i\hbar \frac{d}{dt}{{g}_{m}}(t)={{c}_{m}}(t){{E}_{m}}+\sum\limits_{n}{{}}{{c}_{n}}(t)\left\langle  m \right|{{{\hat{H}}}^{1}}(t)\left| n \right\rangle  \\

& \Rightarrow i\hbar \frac{d}{dt}{{g}_{m}}(t)={{e}^{\left( i\frac{{{E}_{m}}t}{\hbar } \right)}}\sum\limits_{n}{{}}{{c}_{n}}(t)\left\langle  m \right|{{{\hat{H}}}^{1}}(t)\left| n \right\rangle  \\

\end{align}

TeX (checked):

{\begin{aligned}&{{c}_{m}}(t){{E}_{m}}+{{e}^{-\left(i{\frac {{{E}_{m}}t}{\hbar }}\right)}}i\hbar {\frac {d}{dt}}{{g}_{m}}(t)={{c}_{m}}(t){{E}_{m}}+\sum \limits _{n}{}{{c}_{n}}(t)\left\langle m\right|{{\hat {H}}^{1}}(t)\left|n\right\rangle \\&\Rightarrow i\hbar {\frac {d}{dt}}{{g}_{m}}(t)={{e}^{\left(i{\frac {{{E}_{m}}t}{\hbar }}\right)}}\sum \limits _{n}{}{{c}_{n}}(t)\left\langle m\right|{{\hat {H}}^{1}}(t)\left|n\right\rangle \\\end{aligned}}

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MathML (4.052 KB / 551 B) :

cm(t)Em+e(iEmt)iddtgm(t)=cm(t)Em+ncn(t)m|H^1(t)|niddtgm(t)=e(iEmt)ncn(t)m|H^1(t)|n
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