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Quantum Harmonic Oscillator

  1. Nov 2, 2011 #1
    1. The problem statement, all variables and given/known data

    Consider the Hamiltonian

    [tex]H=\frac{p^2}{2M}+\frac{1}{2}\omega^2r^2-\omega_z L_z[/tex]

    Determine its eigenstates and energies.

    2. The attempt at a solution

    I want to check my comprehension; by eigenstate they mean

    [tex]\psi(r)[/tex]
    from the good old

    [tex]H\psi(r)=E\psi(r)[/tex]
    and then the energies would then be solutions for E?
     
  2. jcsd
  3. Nov 2, 2011 #2
    To sort of answer my own question the eigenstates would more properly probably be
    [tex]|\psi>[/tex]
    in
    [tex]H|\psi>=E|\psi>[/tex]
     
  4. Nov 2, 2011 #3

    vela

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    It's a three-dimensional problem, so the wave function will be a function of r, θ, and φ.
     
  5. Nov 2, 2011 #4
    Ah, right. (and just as I was getting comfortable in 2D)
     
  6. Nov 3, 2011 #5

    dextercioby

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    Convert L_z and p to spherical coordinates and separate variables just like in the H-atom case, or the isotropic 3D oscillator.
     
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