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Homework Help: Question about L.S component of hamiltonian

  1. Jun 8, 2013 #1
    1. The problem statement, all variables and given/known data

    I need to find the energies of the lowest level of the following hamiltonian

    H = p^2/2m + (mw^2r^2)/2 + L.S

    (spin 1/2 particle of mass m)

    The tridimensional harmonic oscilator with a coupling term

    2. Relevant equations

    The first two terms are solved, my question is about the term L.S, which l correspond to the lowest energy? l=0 or l= 1? First, I thought that it should be l=0, but in my class they stated l=1, is it related to the heisenberg principle?

    3. The attempt at a solution

    If the hamiltonian was the free particle with just the term L.S i think l = 0 would follow to a fundamental state of 0 energy and it is wrong (i think)...could you help me please?
  2. jcsd
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