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Display information for equation id:math.1737.20 on revision:1737

* Page found: Induzierte Emission und Absorption von Lichtquanten in Atomen (eq math.1737.20)

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Induzierte Emission und Absorption von Lichtquanten in Atomen Eq: math.1737.20

Hash: 40ff7cd36d0c9a86652e07f8f61c57aa

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\begin{align}
& {{W}_{nn0}}=\frac{\pi }{2{{\hbar }^{2}}}\int_{0}^{\infty }{d\left( \hbar \omega  \right)}{{\left( {{{\bar{E}}}_{0}}\left( \omega  \right)\cdot {{{\bar{d}}}_{nn0}} \right)}^{2}}\left\{ \delta ({{E}_{n}}-{{E}_{n0}}-\hbar \omega )+\delta ({{E}_{n}}-{{E}_{n0}}+\hbar \omega ) \right\} \\
& \Rightarrow {{W}_{nn0}}=\frac{\pi }{2{{\hbar }^{2}}}{{\left( {{{\bar{E}}}_{0}}\left( \frac{\left( \left| {{E}_{n}}-{{E}_{n0}} \right| \right)}{\hbar } \right)\cdot {{{\bar{d}}}_{nn0}} \right)}^{2}} \\
& {{{\bar{d}}}_{nn0}}=e\left\langle  n \right|\hat{\bar{r}}\left| {{n}_{0}} \right\rangle  \\
\end{align}

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\begin{aligned} W_{n n 0} = \frac{π}{2 ℏ^{2}} \int_{0}^{\infty} d (ℏ ω) {({\bar{E}}_{0} (ω) \cdot {\bar{d}}_{n n 0})}^{2} {δ (E_{n} - E_{n 0} - ℏ ω) + δ (E_{n} - E_{n 0} + ℏ ω)} \\ \Rightarrow W_{n n 0} = \frac{π}{2 ℏ^{2}} {({\bar{E}}_{0} (\frac{(| E_{n} - E_{n 0} |)}{ℏ}) \cdot {\bar{d}}_{n n 0})}^{2} \\ {\bar{d}}_{n n 0} = e ⟨ n | \hat{\bar{r}} | n_{0} ⟩ \end{aligned}

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