Two identical non-interacting particles

[CaptainQuaser]

Two identical non-interacting particles are in an isotropic harmonic potential. Show that the degeneracies of the three lowest energy levels are:

a) 1, 12, 39 for spin 1/2 (aka fermi)

b)6, 27, 99 for spin 1 (aka bose)

The Attempt at a Solution

Well, I tried counting the states for E_{nl}, noting that no two fermi particles can be in the same state, but two bose particles can be, don't really know where do go from there.

 

[Meir Achuz]

Use S, L, and J.
For instance, S can be 0 or 2 for two spin one bosons with L=0.
This gives six states.