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Display information for equation id:math.2569.39 on revision:2569

* Page found: Das Photonengas im Strahlungshohlraum (eq math.2569.39)

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Das Photonengas im Strahlungshohlraum Eq: math.2569.39

Hash: b6038af9c6e10370f3edbb7e78bc01b6

TeX (original user input):

\begin{align}

& {{B}_{12}}u\left( \nu ,T \right)\left\langle {{N}_{1}} \right\rangle ={{B}_{21}}u\left( \nu ,T \right)\left\langle {{N}_{2}} \right\rangle +{{A}_{21}}\left\langle {{N}_{2}} \right\rangle  \\

& \Rightarrow u\left( \nu ,T \right)=\frac{{{A}_{21}}}{{{B}_{12}}\frac{\left\langle {{N}_{1}} \right\rangle }{\left\langle {{N}_{2}} \right\rangle }-{{B}_{21}}}=\frac{{{A}_{21}}}{{{B}_{12}}\frac{{{g}_{1}}}{{{g}_{2}}}{{e}^{\beta h\nu }}-{{B}_{21}}} \\

\end{align}

TeX (checked):

{\begin{aligned}&{{B}_{12}}u\left(\nu ,T\right)\left\langle {{N}_{1}}\right\rangle ={{B}_{21}}u\left(\nu ,T\right)\left\langle {{N}_{2}}\right\rangle +{{A}_{21}}\left\langle {{N}_{2}}\right\rangle \\&\Rightarrow u\left(\nu ,T\right)={\frac {{A}_{21}}{{{B}_{12}}{\frac {\left\langle {{N}_{1}}\right\rangle }{\left\langle {{N}_{2}}\right\rangle }}-{{B}_{21}}}}={\frac {{A}_{21}}{{{B}_{12}}{\frac {{g}_{1}}{{g}_{2}}}{{e}^{\beta h\nu }}-{{B}_{21}}}}\\\end{aligned}}

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\begin{aligned} B_{12} u (ν, T) ⟨ N_{1} ⟩ = B_{21} u (ν, T) ⟨ N_{2} ⟩ + A_{21} ⟨ N_{2} ⟩ \\ \Rightarrow u (ν, T) = \frac{A_{21}}{B_{12} \frac{⟨ N_{1} ⟩}{⟨ N_{2} ⟩} - B_{21}} = \frac{A_{21}}{B_{12} \frac{g_{1}}{g_{2}} e^{β h ν} - B_{21}} \end{aligned}

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Identifiers

$B_{12}$

$u$

$ν$

$T$

$N_{1}$

$B_{21}$

$u$

$ν$

$T$

$N_{2}$

$A_{21}$

$N_{2}$

$u$

$ν$

$T$

$A_{21}$

$B_{12}$

$N_{1}$

$N_{2}$

$B_{21}$

$A_{21}$

$B_{12}$

$g_{1}$

$g_{2}$

$e$

$β$

$h$

$ν$

$B_{21}$

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