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Homework Help: Two identical non-interacting particles

  1. Apr 12, 2007 #1
    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)

    3. The attempt at a solution

    Well, I tried counting the states for [itex]E_{nl}[/itex], 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.
  2. jcsd
  3. Apr 13, 2007 #2

    Meir Achuz

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    Gold Member

    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.
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