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Display information for equation id:math.1724.12 on revision:1724

* Page found: Zeitabhängige Störungsrechnung (eq math.1724.12)

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Zeitabhängige Störungsrechnung Eq: math.1732.13

Hash: b5946435815715ea3ae01232c95d7f11

TeX (original user input):

\begin{align}

& \hat{H}{{\left| \Psi  \right\rangle }_{t}}=i\hbar \frac{\partial }{\partial t}{{\left| \Psi  \right\rangle }_{t}} \\

& \Rightarrow \sum\limits_{n}{{}}{{c}_{n}}(t)\hat{H}\left| n \right\rangle =i\hbar \sum\limits_{n}{{}}\frac{d}{dt}{{c}_{n}}(t)\left| n \right\rangle =\sum\limits_{n}{{}}{{c}_{n}}(t)\left( {{{\hat{H}}}_{0}}+{{{\hat{H}}}^{1}}(t) \right)\left| n \right\rangle =\sum\limits_{n}{{}}{{c}_{n}}(t)\left( {{E}_{n}}+{{{\hat{H}}}^{1}}(t) \right)\left| n \right\rangle  \\

\end{align}

TeX (checked):

{\begin{aligned}&{\hat {H}}{{\left|\Psi \right\rangle }_{t}}=i\hbar {\frac {\partial }{\partial t}}{{\left|\Psi \right\rangle }_{t}}\\&\Rightarrow \sum \limits _{n}{}{{c}_{n}}(t){\hat {H}}\left|n\right\rangle =i\hbar \sum \limits _{n}{}{\frac {d}{dt}}{{c}_{n}}(t)\left|n\right\rangle =\sum \limits _{n}{}{{c}_{n}}(t)\left({{\hat {H}}_{0}}+{{\hat {H}}^{1}}(t)\right)\left|n\right\rangle =\sum \limits _{n}{}{{c}_{n}}(t)\left({{E}_{n}}+{{\hat {H}}^{1}}(t)\right)\left|n\right\rangle \\\end{aligned}}

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\begin{aligned} \hat{H} {| Ψ ⟩}_{t} = i ℏ \frac{\partial}{\partial t} {| Ψ ⟩}_{t} \\ \Rightarrow \sum_{n} c_{n} (t) \hat{H} | n ⟩ = i ℏ \sum_{n} \frac{d}{d t} c_{n} (t) | n ⟩ = \sum_{n} c_{n} (t) ({\hat{H}}_{0} + {\hat{H}}^{1} (t)) | n ⟩ = \sum_{n} c_{n} (t) (E_{n} + {\hat{H}}^{1} (t)) | n ⟩ \end{aligned}

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Identifiers

$\hat{H}$

$Ψ_{t}$

$i$

$t$

$Ψ_{t}$

$n$

$c_{n}$

$t$

$\hat{H}$

$n$

$i$

$n$

$d$

$d$

$t$

$c_{n}$

$t$

$n$

$n$

$c_{n}$

$t$

${\hat{H}}_{0}$

$\hat{H}$

$t$

$n$

$n$

$c_{n}$

$t$

$E_{n}$

$\hat{H}$

$t$

$n$

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