DEGENERATE FERMIONS - MEAN ENERGIES:
Show that for a non-relativistic 3-dimensional Fermi gas at
temperature T = 0, the mean energy per fermion is given by hi = 3EF
/5.
(ii) Now find out what is hi for a 3-dimensional Fermi gas at
temperature T = 0 in the extreme relativistic limit, ie., the
typical momentum of the fermions satisfies p mc.
(iii) Finally, suppose we now have a 2-dimensional Fermi gas at
T = 0. Find the mean energy per fermion in this case, both in the
non-relativistic and relativistic limits.