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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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\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}

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W n ⁢ n ⁢ 0 = 2 ⁢ π ℏ ⁢ | ⟨ n | F ^ | n 0 ⟩ | 2 ⁢ δ ⁢ ( E n - E n ⁢ 0 - ℏ ⁢ ω ) + 2 ⁢ π ℏ ⁢ | ⟨ n 0 | F ^ + | n ⟩ | 2 ⁢ δ ⁢ ( E n - E n ⁢ 0 + ℏ ⁢ ω ) W n ⁢ n ⁢ 0 = 2 ⁢ π ℏ ⁢ ( e 2 ⁢ m ) 2 ⁢ { | ⟨ n | e i ⁢ k ¯ ⁢ r ¯ ⁢ A ¯ 0 ⁢ p ¯ ^ | n 0 ⟩ | 2 ⁢ δ ⁢ ( E n - E n ⁢ 0 - ℏ ⁢ ω ) + | ⟨ n 0 | e - i ⁢ k ¯ ⁢ r ¯ ⁢ A ¯ 0 ⁢ p ¯ ^ | n ⟩ | 2 ⁢ δ ⁢ ( E n - E n ⁢ 0 + ℏ ⁢ ω ) } absent subscript 𝑊 𝑛 𝑛 0 2 𝜋 Planck-constant-over-2-pi superscript quantum-operator-product 𝑛 ^ 𝐹 subscript 𝑛 0 2 𝛿 subscript 𝐸 𝑛 subscript 𝐸 𝑛 0 Planck-constant-over-2-pi 𝜔 2 𝜋 Planck-constant-over-2-pi superscript quantum-operator-product subscript 𝑛 0 superscript ^ 𝐹 𝑛 2 𝛿 subscript 𝐸 𝑛 subscript 𝐸 𝑛 0 Planck-constant-over-2-pi 𝜔 missing-subexpression subscript 𝑊 𝑛 𝑛 0 2 𝜋 Planck-constant-over-2-pi superscript 𝑒 2 𝑚 2 superscript quantum-operator-product 𝑛 superscript 𝑒 𝑖 ¯ 𝑘 ¯ 𝑟 subscript ¯ 𝐴 0 ^ ¯ 𝑝 subscript 𝑛 0 2 𝛿 subscript 𝐸 𝑛 subscript 𝐸 𝑛 0 Planck-constant-over-2-pi 𝜔 superscript quantum-operator-product subscript 𝑛 0 superscript 𝑒 𝑖 ¯ 𝑘 ¯ 𝑟 subscript ¯ 𝐴 0 ^ ¯ 𝑝 𝑛 2 𝛿 subscript 𝐸 𝑛 subscript 𝐸 𝑛 0 Planck-constant-over-2-pi 𝜔 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle{{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)\\ &\displaystyle{{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}_{n% 0}}-\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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Wnn0=2πℏ|⟨n|F^|n0⟩|2δ(En−En0−ℏω)+2πℏ|⟨n0|F^+|n⟩|2δ(En−En0+ℏω)Wnn0=2πℏ(e2m)2{|⟨n|eik¯r¯A¯0p¯^|n0⟩|2δ(En−En0−ℏω)+|⟨n0|e−ik¯r¯A¯0p¯^|n⟩|2δ(En−En0+ℏω)}

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