# Tag Info

I will present the result for the one-dimensional case only. It is readily generalized to your three-dimensional situation. Knowing the phonon dispersion $\omega(q)$, the DOS can be defined as $$D(\omega) = \frac{1}{2\pi}\int\mathrm{d}q\,\delta(\omega-\omega(q)).$$ Using the formal identity $$\delta(g(x)) = \sum_{i}\frac{\delta(x-x_i)}{|g'(x_i)|}$$ where ...