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Display information for equation id:math.1734.11 on revision:1734

* Page found: Induzierte Emission und Absorption von Lichtquanten in Atomen (eq math.1734.11)

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Induzierte Emission und Absorption von Lichtquanten in Atomen Eq: math.1737.11

Hash: e06aa3b4dfd145865224f4369d9f5fd0

TeX (original user input):

\begin{align}
& -\frac{e}{m}\left\langle  n \right|{{e}^{i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}\left| {{n}_{0}} \right\rangle \cong -\frac{i}{\hbar }\frac{em}{2m}{{{\bar{A}}}_{0}}\left\langle  n \right|{{{\hat{H}}}_{0}}\hat{\bar{r}}-\hat{\bar{r}}{{{\hat{H}}}_{0}}\left| {{n}_{0}} \right\rangle =-\frac{i}{2\hbar }({{E}_{n}}-{{E}_{n0}}){{{\bar{A}}}_{0}}e\left\langle  n \right|\hat{\bar{r}}\left| {{n}_{0}} \right\rangle  \\
& {{{\bar{A}}}_{0}}=-\frac{{{{\bar{E}}}_{0}}}{\omega } \\
& e\left\langle  n \right|\hat{\bar{r}}\left| {{n}_{0}} \right\rangle :={{{\bar{d}}}_{nn0}} \\
\end{align}

TeX (checked):

{\begin{aligned}&-{\frac {e}{m}}\left\langle n\right|{{e}^{i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}\left|{{n}_{0}}\right\rangle \cong -{\frac {i}{\hbar }}{\frac {em}{2m}}{{\bar {A}}_{0}}\left\langle n\right|{{\hat {H}}_{0}}{\hat {\bar {r}}}-{\hat {\bar {r}}}{{\hat {H}}_{0}}\left|{{n}_{0}}\right\rangle =-{\frac {i}{2\hbar }}({{E}_{n}}-{{E}_{n0}}){{\bar {A}}_{0}}e\left\langle n\right|{\hat {\bar {r}}}\left|{{n}_{0}}\right\rangle \\&{{\bar {A}}_{0}}=-{\frac {{\bar {E}}_{0}}{\omega }}\\&e\left\langle n\right|{\hat {\bar {r}}}\left|{{n}_{0}}\right\rangle :={{\bar {d}}_{nn0}}\\\end{aligned}}

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\begin{matrix} - \frac{e}{m} ⟨ n | e^{i \bar{k} \bar{r}} {\bar{A}}_{0} \hat{\bar{p}} | n_{0} ⟩ ≅ - \frac{i}{ℏ} \frac{e m}{2 m} {\bar{A}}_{0} ⟨ n | {\hat{H}}_{0} \hat{\bar{r}} - \hat{\bar{r}} {\hat{H}}_{0} | n_{0} ⟩ = - \frac{i}{2 ℏ} (E_{n} - E_{n 0}) {\bar{A}}_{0} e ⟨ n | \hat{\bar{r}} | n_{0} ⟩ \\ {\bar{A}}_{0} = - \frac{{\bar{E}}_{0}}{ω} \\ e ⟨ n | \hat{\bar{r}} | n_{0} ⟩ := {\bar{d}}_{n n 0} \end{matrix}

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Identifiers

$e$

$m$

$n$

$e$

$i$

$\bar{k}$

$\bar{r}$

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

$\hat{\bar{p}}$

$n_{0}$

$i$

$e$

$m$

$m$

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

$n$

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

$\hat{\bar{r}}$

$\hat{\bar{r}}$

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

$n_{0}$

$i$

$E_{n}$

$E_{n 0}$

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

$e$

$n$

$\hat{\bar{r}}$

$n_{0}$

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

${\bar{E}}_{0}$

$ω$

$e$

$n$

$\hat{\bar{r}}$

$n_{0}$

${\bar{d}}_{n n 0}$

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