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7.2
Consider an anisotropic harmonic oscillator described by the Hamiltonian
1
H =
2µ
-(p; + p; + p?) + ;kı (x² + y³) +
(a) Find the energy levels and the corresponding energy eigenfunctions using
Cartesian coordinates. What are the degeneracies of the levels, assuming that
wj = (k¡/µ)'/2 and wz =
(b) Can the stationary states be eigenstates of L²? of L¿?
(k2/µ)/² are incommensurable?

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