Problem set 10

This will round off chapter 5, and we'll start on chapter 6 the following week.

For solutions see Sections 5.3 and 5.6 in the compendium. To derive the Debye density of states use the dispersion relation $\omega=vk$, with $k$ the magnitude of the wave vector, and that the momentum of a wave is $p=\hbar k$. Also, remember that in equation (5.60) 3N is the number of modes, which is distinct from the number of phonons (for example, at T=0 there are no vibrations and thus no phonons, while the number of modes that can be excited is 3N always).