Consider an isotropic harmonic oscillator in two dimensions. The Hamiltonian is given by (a) What are the
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Consider an isotropic harmonic oscillator in two dimensions. The Hamiltonian is given by
(a) What are the energies of the three lowest-lying states? Is there any degeneracy?
(b) We now apply a perturbation
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, the unperturbed energy obtained in (a) plus the first-order energy shift] for each of the three lowest-lying states.
(c) Solve the H0 + V problem exactly. Compare with the perturbation results obtained in (b). [You may use 
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a Energies of the Three LowestLying States without Perturbation The Hamiltonian for the isotropic ha...View the full answer
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