1. Consider a particle of mass m in a two-dimensional harmonic oscillator potential p² 1 Ho= -+-mw²(x² + y²) 2m to which is added a perturbation H' = emw²xy. The unperturbed 2nd excited state is three-fold degenerate. (a) Find the first-order corrections to the energy. (b) Find the "good" states (express them as a linear combination of wave functions of the unperturbed Hamiltonian).

1. Consider a particle of mass m in a two-dimensional harmonic oscillator potential p² 1 Ho= -+-mw²(x² + y²) 2m to which is added a perturbation H' = emw²xy. The unperturbed 2nd excited state is three-fold degenerate. (a) Find the first-order corrections to the energy. (b) Find the "good" states (express them as a linear combination of wave functions of the unperturbed Hamiltonian).