Quantum Statistics

a. Show that the density of states of a 2-D Fermi gas in a rectangular solid of dimension L2 equals

N(E) =  

b. Show that the chemical potential of a Fermi gas in 2 dimensions is given by



for n electrons per unit area.  Use an integral table to solve the integral and watch your limits of integration.

c. Show that for all small T, μ becomes independent of T.  

(See attachment for proper display of equations, symbols)