diff --git a/src/8_many_atoms_solutions.md b/src/8_many_atoms_solutions.md index b20a3a3b0485cdadb35e0ad8e714312f5815c2ed..7abc667789264b43fc8fd0aadb8466150ad15d30 100644 --- a/src/8_many_atoms_solutions.md +++ b/src/8_many_atoms_solutions.md @@ -25,7 +25,7 @@ Optical branch corresponds with (+) in the equation given in the lecture notes. ### Subquestion 3 -Density of states is given as $g(\omega) = \frac{dN}{d\omega} = \frac{dN}{dk}\frac{dk}{d\omega}$. We know $\frac{dN}{dk} = 2\frac{L}{2\pi} = \frac{L}{\pi}$ since we have 1D and positive and negative k-values. $\frac{dk}{d\omega}$ can be computed using the group velocity: $$\frac{dk}{d\omega} = \bigg(\frac{d\omega}{dk} \bigg)^{-1} = (v_g)^{-1}$$ +Density of states is given as $g(\omega) = \frac{dN}{d\omega} = \frac{dN}{dk}\frac{dk}{d\omega}$. We know $\frac{dN}{dk} = \frac{L}{2\pi}$ since we have 1D. $\frac{dk}{d\omega}$ can be computed using the group velocity: $$\frac{dk}{d\omega} = \bigg(\frac{d\omega}{dk} \bigg)^{-1} = (v_g)^{-1}$$ ## Exercise 2: the Peierls transition