of 1
University California, Berkeley
Physics H7C Fall 1999 (Strovink)
PROBLEM SET 12
1.
Rohlf 12.5.
6.
Rohlf 18.11.
2.
N electrons each of mass m are conned within
a (formerly) cubic innite potential well that has
been squashed almost at: V = 0 for (0 < x <
L and 0 < y < L and 0 < z < L), V = otherwise. Here
1 (cube is squashed in the
z direction) and N
1. The electrons do not
interact with each other and are at very low temperature so that they ll up the available states
in order of increasing energy. Take N
1, so
that the z part of each electrons wavefunction
may be assumed to be the same (lowest possible kz ). Thus the problem is reduced to two
dimensions. Calculate the dierence energy between
the of the most energetic electron (Fermi
energy) and the energy of a ground state electron, using the approximation N
1. should
depend on m, N , and L, but not .
7.
Rohlf 19.18.
3.
Write an integral equation for the fraction F of
nonrelativistic fermions in a gas at nite temperature T which have energy above the Fermi
energy EF . The density of states is proportional to E 1/2 and the probability that a state
is occupied is
1
exp (E EF ) + 1
where = (kT )1 . You dont need to perform
the integration, but you should set up the integral so that doing it would yield the correct answer without any additional physical reasoning.
4.
Rohlf 12.16.
5.
Rohlf 17.27.
8.
Rohlf 19.29.