Homework Set # 12 – Not Due – Solution will be provided on November 29.

1. An ideal Fermi gas is at rest at absolute zero and has a Fermi energy μ. The mas of each particle is m. If v denotes the velocity of a molecule, find <v_x> and <v_x²>.

2. Consider an ideal gas of N electrons in a volume V at absolute zero.

• a) Calculate the total mean energy <E> of this gas.

• b) Express <E> in terms of the Fermi energy μ.

• c) Show that <E> is properly an extensive quantity, but that for a fixed volume V, <E> is not proportional to the number N of particles in the container. How do you account for this last result despite the fact that there is no interaction potential potential between the particles?

3. Derive Eq.(8.1.9) Hint: use Eq.(8.1.4) and recurrence formula (E.6).

4. Problem 8.14 (solve it only for T=0.

5. Problem 8.15