Exercise 67 calculates the minimum total energy in a system of spin4 fermions and is appli...

Exercise 67 calculates the minimum total energy in a system of spin4 fermions and is applicable to conduction electrons in a metal. The average particle energy is the total energy divided by the number of particles N. Show that the average particle energy  of a conduction electron at low temperature (T  0) is (3/5)EF. This form is convenient, being rather simple, and it can easily be put in terms of N, V, and m via equation (9-42).