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Display information for equation id:math.1734.6 on revision:1734

* Page found: Induzierte Emission und Absorption von Lichtquanten in Atomen (eq math.1734.6)

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Induzierte Emission und Absorption von Lichtquanten in Atomen Eq: math.1737.6

Hash: 081f17c0f196edbf42ca3b8f8f60067b

TeX (original user input):

\begin{align}

& \hat{H}={{{\hat{H}}}_{0}}-\frac{e}{m}\bar{A}\cdot \hat{\bar{p}}={{{\hat{H}}}_{0}}+{{{\hat{H}}}^{1}} \\

& {{{\hat{H}}}^{1}}:=-\frac{e}{m}\cos (\bar{k}\bar{r}-\omega t){{{\bar{A}}}_{0}}\hat{\bar{p}}=-\frac{e}{2m}{{e}^{i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}{{e}^{-i\omega t}}-\frac{e}{2m}{{e}^{-i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}{{e}^{i\omega t}} \\

& -\frac{e}{2m}{{e}^{i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}:=\hat{F} \\

& -\frac{e}{2m}{{e}^{-i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}:={{{\hat{F}}}^{+}} \\

& {{{\hat{H}}}^{1}}=\hat{F}{{e}^{-i\omega t}}+{{{\hat{F}}}^{+}}{{e}^{i\omega t}} \\

\end{align}

TeX (checked):

{\begin{aligned}&{\hat {H}}={{\hat {H}}_{0}}-{\frac {e}{m}}{\bar {A}}\cdot {\hat {\bar {p}}}={{\hat {H}}_{0}}+{{\hat {H}}^{1}}\\&{{\hat {H}}^{1}}:=-{\frac {e}{m}}\cos({\bar {k}}{\bar {r}}-\omega t){{\bar {A}}_{0}}{\hat {\bar {p}}}=-{\frac {e}{2m}}{{e}^{i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}{{e}^{-i\omega t}}-{\frac {e}{2m}}{{e}^{-i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}{{e}^{i\omega t}}\\&-{\frac {e}{2m}}{{e}^{i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}:={\hat {F}}\\&-{\frac {e}{2m}}{{e}^{-i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}:={{\hat {F}}^{+}}\\&{{\hat {H}}^{1}}={\hat {F}}{{e}^{-i\omega t}}+{{\hat {F}}^{+}}{{e}^{i\omega t}}\\\end{aligned}}

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\begin{matrix} \hat{H} = {\hat{H}}_{0} - \frac{e}{m} \bar{A} \cdot \hat{\bar{p}} = {\hat{H}}_{0} + {\hat{H}}^{1} \\ {\hat{H}}^{1} := - \frac{e}{m} \cos (\bar{k} \bar{r} - ω t) {\bar{A}}_{0} \hat{\bar{p}} = - \frac{e}{2 m} e^{i \bar{k} \bar{r}} {\bar{A}}_{0} \hat{\bar{p}} e^{- i ω t} - \frac{e}{2 m} e^{- i \bar{k} \bar{r}} {\bar{A}}_{0} \hat{\bar{p}} e^{i ω t} \\ - \frac{e}{2 m} e^{i \bar{k} \bar{r}} {\bar{A}}_{0} \hat{\bar{p}} := \hat{F} \\ - \frac{e}{2 m} e^{- i \bar{k} \bar{r}} {\bar{A}}_{0} \hat{\bar{p}} := {\hat{F}}^{+} \\ {\hat{H}}^{1} = \hat{F} e^{- i ω t} + {\hat{F}}^{+} e^{i ω t} \end{matrix}

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Identifiers

$\hat{H}$

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

$e$

$m$

$\bar{A}$

$\hat{\bar{p}}$

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

$\hat{H}$

$\hat{H}$

$e$

$m$

$\bar{k}$

$\bar{r}$

$ω$

$t$

${\bar{A}}_{0}$

$\hat{\bar{p}}$

$e$

$m$

$e$

$i$

$\bar{k}$

$\bar{r}$

${\bar{A}}_{0}$

$\hat{\bar{p}}$

$e$

$i$

$ω$

$t$

$e$

$m$

$e$

$i$

$\bar{k}$

$\bar{r}$

${\bar{A}}_{0}$

$\hat{\bar{p}}$

$e$

$i$

$ω$

$t$

$e$

$m$

$e$

$i$

$\bar{k}$

$\bar{r}$

${\bar{A}}_{0}$

$\hat{\bar{p}}$

$\hat{F}$

$e$

$m$

$e$

$i$

$\bar{k}$

$\bar{r}$

${\bar{A}}_{0}$

$\hat{\bar{p}}$

$\hat{F}$

$\hat{H}$

$\hat{F}$

$e$

$i$

$ω$

$t$

$\hat{F}$

$e$

$i$

$ω$

$t$

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