3. Consider an isotropic harmonic oscillator in two dimensions. The Hamiltonian is given by: 門+,1 Ho +m (X² + Y®) 2m (a) What are the energies of the three lowest-lying states? Is there any...

Extracted text: 3. Consider an isotropic harmonic oscillator in two dimensions. The Hamiltonian is given by: 門+,1 Ho +m (X² + Y®) 2m (a) What are the energies of the three lowest-lying states? Is there any degeneracy? (b) Apply a perturbation V = ốmu?XY, where 6 is a dimensionless real mumber much smaller than unity. Find the zeroth-order energy eigenket and the corresponding energy to first order (that is, the unperturbed energy obtained in the previous part plus the first-order energy shift] for each of the three lowest-lying states. (c) Solve the Ho + V problem exactly. Compare with the perturbation results obtained in the second part.