A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

178 SOLUTIONS

Therefore, for asystem consisting of identical particles, and we
may write for

where and From(S.4.69.3) we have

and we recover

b) The number of quantumstates in the intervalbetween and for
a Fermi gas is

where At electronsfill all the stateswithmomentum
from 0 to so thetotal number ofelectronsNis given by

For and

or

The totalenergy of the gas

Substituting from(S.4.69.8), we obtain