@@ -65,5 +65,5 @@ Hint: The group velocity is given as $v = \frac{d\omega}{dk}$, draw a coordinate
### Subquestion 1
For the energy we have $$U = \int \hbar \omega g(\omega) (n(\omega) + \frac{1}{2})d\omega$$ with $g(\omega)$ as in Exercise 1 subquestion 2.
For the energy we have $$U = \int \hbar \omega g(\omega) (n(\omega,T) + \frac{1}{2})d\omega$$ with $g(\omega)$ as in Exercise 1 subquestion 2 and $n(\omega,T) = \frac{1}{e^{\frac{\hbar\omega}{k_BT}}-1}$