= Solution
In the harmonic approximation, sum over <wavevector> $\mathbf q$ and <phonon> branch $s$:
$$
\boxed{U_{la}=\sum_{\mathbf q,s}\hbar\omega_{\mathbf q s}\left[\frac1{e^{\hbar\omega_{\mathbf q s}/k_BT}-1}+\frac12\right].}
$$
The occupation factor is the <Bose-Einstein distribution> with zero <phonon> <chemical potential>; $\tfrac12\hbar\omega$ is the <zero-point energy>. A temperature-independent zero-point term does not contribute to the <heat capacity> in this fixed-frequency approximation.
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