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Display information for equation id:math.2564.11 on revision:2564

* Page found: Das Photonengas im Strahlungshohlraum (eq math.2564.11)

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Das Photonengas im Strahlungshohlraum Eq: math.2569.11

Hash: adb7628bc3d0637e94a039bbd3c97dff

TeX (original user input):

\begin{align}

& 2\sum\limits_{{\bar{q}}}^{{}}{{}}->\frac{2V}{{{h}^{3}}}\int_{{}}^{{}}{{}}{{d}^{3}}\left( \hbar \bar{q} \right)=\frac{8\pi V}{{{\left( 2\pi  \right)}^{3}}}\int_{0}^{\infty }{{}}dq{{q}^{2}}=\frac{8\pi V}{{{\left( 2\pi  \right)}^{3}}{{c}^{3}}}\int_{0}^{\infty }{{}}d\omega {{\omega }^{2}} \\

& \omega =cq \\

& \omega =2\pi \nu  \\

& \Rightarrow \frac{8\pi V}{{{\left( 2\pi  \right)}^{3}}{{c}^{3}}}\int_{0}^{\infty }{{}}d\omega {{\omega }^{2}}=\frac{8\pi V}{{{c}^{3}}}\int_{0}^{\infty }{{}}d\nu {{\nu }^{2}} \\

\end{align}

TeX (checked):

{\begin{aligned}&2\sum \limits _{\bar {q}}^{}{}->{\frac {2V}{{h}^{3}}}\int _{}^{}{}{{d}^{3}}\left(\hbar {\bar {q}}\right)={\frac {8\pi V}{{\left(2\pi \right)}^{3}}}\int _{0}^{\infty }{}dq{{q}^{2}}={\frac {8\pi V}{{{\left(2\pi \right)}^{3}}{{c}^{3}}}}\int _{0}^{\infty }{}d\omega {{\omega }^{2}}\\&\omega =cq\\&\omega =2\pi \nu \\&\Rightarrow {\frac {8\pi V}{{{\left(2\pi \right)}^{3}}{{c}^{3}}}}\int _{0}^{\infty }{}d\omega {{\omega }^{2}}={\frac {8\pi V}{{c}^{3}}}\int _{0}^{\infty }{}d\nu {{\nu }^{2}}\\\end{aligned}}

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\begin{matrix} 2 \sum_{\bar{q}}^{} - > \frac{2 V}{h^{3}} \int_{}^{} d^{3} (ℏ \bar{q}) = \frac{8 π V}{{(2 π)}^{3}} \int_{0}^{\infty} d q q^{2} = \frac{8 π V}{{(2 π)}^{3} c^{3}} \int_{0}^{\infty} d ω ω^{2} \\ ω = c q \\ ω = 2 π ν \\ \Rightarrow \frac{8 π V}{{(2 π)}^{3} c^{3}} \int_{0}^{\infty} d ω ω^{2} = \frac{8 π V}{c^{3}} \int_{0}^{\infty} d ν ν^{2} \end{matrix}

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Identifiers

$\bar{q}$

$V$

$h$

$\bar{q}$

$π$

$V$

$π$

$q$

$q$

$π$

$V$

$π$

$c$

$ω$

$ω$

$ω$

$c$

$q$

$ω$

$π$

$ν$

$π$

$V$

$π$

$c$

$ω$

$ω$

$π$

$V$

$c$

$ν$

$ν$

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