@@ -491,7 +491,7 @@ The dispersion of energy band 1 is $\varepsilon_1(\mathbf{k}) = Ak^2$ and that o
2. Calculate the density of states and sketch it as a function of energy. Hint: the total density of states is obtained by adding the density of states associated with the individual bands.
3. Express the number of electrons in the system in terms of the Fermi energy $E_F$.
4. Express the number of electrons in the energy range $\varepsilon_a<\varepsilon<\varepsilon_b$ as an integral over energy
5. Assuming $\varepsilon_a \gg E_F$, explicitly calculate the integral of the previous subquestion.
5. Assuming $\varepsilon_a - E_F \gg k_B T$, explicitly calculate the integral of the previous subquestion.
[^1]:This is not completely true, as we will see when learning about [semiconductors](13_semiconductors)
[^2]:An[isotropic](https://en.wikipedia.org/wiki/Isotropic_solid) material means that the material is the same in all directions.
