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## 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

[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?