Quantum Harmonic Oscillator

  • #1

Homework Statement

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

from the good old

and then the energies would then be solutions for E?
  • #2
To sort of answer my own question the eigenstates would more properly probably be
  • #3
It's a three-dimensional problem, so the wave function will be a function of r, θ, and φ.
  • #4
Ah, right. (and just as I was getting comfortable in 2D)
  • #5
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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