Two identical particles of mass m are trapped by an external one dimensional harmonic oscillator potential, but do not interact with each other. The energy levels for a single particle in the potential are En = (n + 1/2)(h_bar)(ω) for n = 0,1,2,3,....
(a) What are the possible energy levels of the two particle system?
(b) Calculate the partition function given that the two particles are bosons.
(c) Calculate the partition function given that the two particles are fermions.