PHYS 333
Winter 2009
Assignment 10
Due: 5:00 pm Friday April 17
1. Schroeder 7.16
A system of N (spinless) identical fermions has equally spaced energy levels which are all
nondegenerate. (That is, each level holds only one fermion.)
At low temperatures, it is useful to represent each state of the system by a column of dots,
where a filled dot represents an occupied level, and an open dot represents an unoccupied
level. At low temperatures, all states below a certain level are occupied, and are not shown
on the dotdiagram.
Suppose that the spacing between the levels is
η
, and that
q
is the number of energy units
over and above the groundstate energy
U
0
. That is, the (internal) energy is
U
=
U
0
+
qη
.
The figure shows all possible states for 0
≤
q
≤
3.
q
= 0
1
2
3
(a) Draw dotdiagrams for
q
= 4
,
5 and 6.
(b) Compute, therefore, the probability of each level being occupied when
q
= 6.
Plot a
graph of this probability as a function of the energy of each level, and from the graph,
estimate
μ
and
T
by “fitting” to the FermiDirac distribution.
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 Winter '09
 Harris
 Physics, Energy, Mass, Fundamental physics concepts, Neutron star

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