Hi course,
For the first problem of the tight-binding model exercises I’ve used the relation E=
\hbar \omega and basically substituted that into the expression for group velocity which reads:
v_g = \frac{1}{\hbar} \frac{\partial E}{\partial k} Then from this I got that for phonons we get:
v_g = \frac{1}{\hbar} \frac{\partial (\hbar \omega)}{\partial k}
so the \hbar cancels out and we’re left with v_g = \frac{\partial \omega}{\partial k}. Then I subbed this into the density of states as you can see in my attached picture but I keep getting an extra \hbar that isn’t there in the DOS. What’s going wrong here? (In the final expression there’s \hbar in the denominator)
