Discuss the below:
Partition functions of boxes containing bosons or fermions
Q: Suppose you have a "box" in which each particle may occupy any of 10 single-particle states. For simplicity, assume that each of these states has energy zero.
(a) What is the partition function of this system if the box contains only one particle?
(b) What is the partition function of this system if the box contains two distinguishable particles?
(c) What is the partition function if the box contains two identical bosons?
(d) What is the partition function if the box contains two identical fermions?
(e) What would be the partition function of this system according to equation Z = (1/N!)Z_1^N?
(f) What is the probability of finding both particles in the same single-particle state, for the three cases of distinguishable particles, identical bosons, and identical fermions?