Solutions lecture 7

src/8_many_atoms_sol.md

@@ -25,3 +25,5 @@ Optical branch corresponds with (+) in the equation given in the lecture notes.
 
 ### Subquestion 3
 
+Density of states is given as $g(\omega) = \frac{dN}{d\omega} = \frac{dN}{dk}\frac{dk}{d\omega}$. $\frac{dN}{dk} = \frac{L}{2\pi}$ since we have 1D. $\frac{dk}{d\omega}$ can be computed using the group velocity: $$\frac{dk}{d\omega} = $$
+