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7 Consider an isotropic harmonic oscillator in two dimensions. The Hamiltonian isH0 = (Px^2)/(2m) (Py^2)/(2m) (mω^2)/(2)(x^2 y^2).a. What are the energies of the three lowest-lying states? Is there any degeneracy?b. We now apply a perturbationV = δ mω^2 xy,where δ is a dimensionless real number much smaller than unity. Find the zeroth-order energy eigenket and the corresponding energy to first order [that is, theunperturbed energy obtained in (a) plus the first-order energy shift] for each
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