@@ -269,8 +269,8 @@ The Sommerfeld model provides a good description of free electrons in alkali met
1. Check the [Fermi surface database](fermi_surfaces.md) in the attic. Explain why potassium and (most) other alkali metals can be described well with the Sommerfeld model.
2. Calculate the Fermi temperature, Fermi wave vector and Fermi velocity for potassium.
3. Why is the Fermi temperature much higher than room temperature?
4. Calculate the free electron density in Potassium.
5. Compare this with the actual electron density of Potassium, which can be calculated by using the density, atomic mass and atomic number of Potassium. What can you conclude from this?
4. Calculate the free electron density in potassium.
5. Compare this with the actual electron density of potassium, which can be calculated by using the density, atomic mass and atomic number of potassium. What can you conclude from this?
#### Exercise 2: the $n$-dimensional free electron model.
In the lecture, it has been explained that the density of states (DOS) of the free electron model is proportional to $1/\sqrt{\epsilon}$ in 1D, constant in 2D and proportional to $\sqrt{\epsilon}$ in 3D. In this exercise, we are going to derive the DOS of the free electron model for an arbitrary number of dimensions.
