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Commit fb926c1f authored by T. van der Sar's avatar T. van der Sar
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Update 2_debye_model.md

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......@@ -169,7 +169,7 @@ $$
\begin{align}
E &= \frac{L^3}{(2\pi)^3}\int\limits_0^{2π}d\varphi\int\limits_0^π \sin θ\;\int\limits_0^∞ k^2 dk × 3 × \left(\frac{1}{2}\hbar\omega(k)+\frac{\hbar\omega(k)}{ {\rm e}^{\hbar\omega(k)/{k_B T}}-1}\right)\\
&= \frac{L^3}{(2\pi)^3}\int_0^∞ 12 π k^2 dk \left(\frac{1}{2}\hbar\omega(k)+\frac{\hbar\omega(k)}{ {\rm e}^{\hbar\omega(k)/{k_{\rm B}T}}-1}\right)\\
&= \frac{L^3}{(2\pi)^3}\int_0^∞ 12 π v{\rm s}^{-3} \omega^2 d\omega \left(\frac{1}{2}\hbar\omega+\frac{\hbar\omega}{ {\rm e}^{\hbar\omega/{k_{\rm B}T}}-1}\right).
&= \frac{L^3}{(2\pi)^3}\int_0^∞ 12 π v_{\rm s}^{-3} \omega^2 d\omega \left(\frac{1}{2}\hbar\omega+\frac{\hbar\omega}{ {\rm e}^{\hbar\omega/{k_{\rm B}T}}-1}\right).
\end{align}
$$
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