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Display information for equation id:math.1737.7 on revision:1737

* Page found: Induzierte Emission und Absorption von Lichtquanten in Atomen (eq math.1737.7)

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Induzierte Emission und Absorption von Lichtquanten in Atomen Eq: math.1737.7

Hash: 1d6adfbf8410f5cdb3def350df302eaa

TeX (original user input):

\begin{align}

& {{W}_{nn0}}=\frac{2\pi }{\hbar }{{\left| \left\langle  n \right|\hat{F}\left| {{n}_{0}} \right\rangle  \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}-\hbar \omega )+\frac{2\pi }{\hbar }{{\left| \left\langle  {{n}_{0}} \right|{{{\hat{F}}}^{+}}\left| n \right\rangle  \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}+\hbar \omega ) \\
& {{W}_{nn0}}=\frac{2\pi }{\hbar }{{\left( \frac{e}{2m} \right)}^{2}}\left\{ {{\left| \left\langle  n \right|{{e}^{i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}\left| {{n}_{0}} \right\rangle  \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}-\hbar \omega )+{{\left| \left\langle  {{n}_{0}} \right|{{e}^{-i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}\left| n \right\rangle  \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}+\hbar \omega ) \right\} \\
\end{align}

TeX (checked):

{\begin{aligned}&{{W}_{nn0}}={\frac {2\pi }{\hbar }}{{\left|\left\langle n\right|{\hat {F}}\left|{{n}_{0}}\right\rangle \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}-\hbar \omega )+{\frac {2\pi }{\hbar }}{{\left|\left\langle {{n}_{0}}\right|{{\hat {F}}^{+}}\left|n\right\rangle \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}+\hbar \omega )\\&{{W}_{nn0}}={\frac {2\pi }{\hbar }}{{\left({\frac {e}{2m}}\right)}^{2}}\left\{{{\left|\left\langle n\right|{{e}^{i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}\left|{{n}_{0}}\right\rangle \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}-\hbar \omega )+{{\left|\left\langle {{n}_{0}}\right|{{e}^{-i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}\left|n\right\rangle \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}+\hbar \omega )\right\}\\\end{aligned}}

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\begin{aligned} W_{n n 0} = \frac{2 π}{ℏ} {| ⟨ n | \hat{F} | n_{0} ⟩ |}^{2} δ (E_{n} - E_{n 0} - ℏ ω) + \frac{2 π}{ℏ} {| ⟨ n_{0} | {\hat{F}}^{+} | n ⟩ |}^{2} δ (E_{n} - E_{n 0} + ℏ ω) \\ W_{n n 0} = \frac{2 π}{ℏ} {(\frac{e}{2 m})}^{2} {{| ⟨ n | e^{i \bar{k} \bar{r}} {\bar{A}}_{0} \hat{\bar{p}} | n_{0} ⟩ |}^{2} δ (E_{n} - E_{n 0} - ℏ ω) + {| ⟨ n_{0} | e^{- i \bar{k} \bar{r}} {\bar{A}}_{0} \hat{\bar{p}} | n ⟩ |}^{2} δ (E_{n} - E_{n 0} + ℏ ω)} \end{aligned}

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Translations to Computer Algebra Systems

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Identifiers

$W_{n n 0}$

$π$

$n$

$\hat{F}$

$n_{0}$

$δ$

$E_{n}$

$E_{n 0}$

$ω$

$π$

$n_{0}$

$\hat{F}$

$n$

$δ$

$E_{n}$

$E_{n 0}$

$ω$

$W_{n n 0}$

$π$

$e$

$m$

$n$

$e$

$i$

$\bar{k}$

$\bar{r}$

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

$\hat{\bar{p}}$

$n_{0}$

$δ$

$E_{n}$

$E_{n 0}$

$ω$

$n_{0}$

$e$

$i$

$\bar{k}$

$\bar{r}$

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

$\hat{\bar{p}}$

$n$

$δ$

$E_{n}$

$E_{n 0}$

$ω$

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