Calculate the partition function of an ideal gas of n = 3 identical fermions in equilibrium with a heat bath at temperature t. assume that each particle can be in one of four possible states with energies, ; ; and .
find a. the partition function
b. the mean number of particles in
c. the mean energy of the system when in contact with a heat reservoir at temperature t.
d. repeat all the points above if the 3 particles are bosons