@@ -466,7 +466,7 @@ Using the answer for 1, find $g(k)$ for 1D, 2D and 3D.
7. Work out these integrals for $T = 0$.
### Exercise 3: a hypothetical material
A hypothetical metal has a Fermi energy $\varepsilon_F = 5.2 \,\mathrm{eV}$ and a density of states per unit volume $g(\varepsilon) = 2 \times 10^{10} \,\mathrm{eV}^{-\frac{3}{2}} \sqrt{\varepsilon}$.
A hypothetical metal has a Fermi energy $\varepsilon_F = 5.2 \,\mathrm{eV}$ and a density of states $g(\varepsilon) = 2 \times 10^{10} \,\mathrm{eV}^{-\frac{3}{2}} \sqrt{\varepsilon}$.
1. Give an integral expression for the total energy of the electrons in this hypothetical material in terms of the density of states $g(\varepsilon)$, the temperature $T$ and the chemical potential $\mu = \varepsilon_F$.