Three non-interacting particles of mass m are placed in a harmonic oscillator potential of frequency ω. It is known that the total energy of the system is 15/2 ħω. Write down all configurations that would result in this total energy. Find the most probable configuration and the most probable single particle energy. Verify that the general case expressions for Q(N1, N2, N3 ...) are correct for this special case. Do this for:
a. distinguishable particles
b. spin-1/2 fermions
c. spin-0 bosons