Configuration
0
XX
Number of states
?
3?
MB
BE
1
1
FD
0
X
X
2
1
1
Problem Q1:
Consider a system consisting of two particles, each of which can be in any one of three
quantum states of respective energies, 0, ?, and 3?. You can consider the chemical potential, ?,
to be zero and the system to be in contact with a reservoir of temperature, T.
a) (10 points) Fill out the above table (note that a couple of rows have been filled out for you)
showing the possible states of each particle and the number of possible states if we consider
the particles as classical, distinguishable particles, (following Maxwell-Boltzman statistics
(MB))., Bose-Einstein statistics (BE) or Fermi-Dirac statistics (FD).
b) (10 points) Starting with $Z = \sum_{states} e^{-\beta E(s)}$, form an expression for Z in the MB case.
c) (10 points) Starting with $Z = \sum_{states} e^{-\beta E(s)}$, form an expression for Z in the BE case.
d) (10 points) Starting with $Z = \sum_{states} e^{-\beta E(s)}$, form an expression for Z in the FD case.
