Consider a system consisting of two particles, each of which can be in any one of three quantum states of respective energies 0, e and 3e. The system is in contact with a heat reservoir at temperature T=(Kβ)^-1. Since the number of particles is fixed, there is no need to consider the chemical potential.


a) Write an expression for the partition function Z if the particles obey classical Maxwell Boltzmann statistics and are considered distinguishable. You’ll need to enumerate all the states and sum over all of them.

b) What is Z if the particles obey Bose-Einstein statistics?

c) What is Z if the particles obey Fermi-Dirac statistics?