Consider a spinless particle of charge q and mass m constrained to move in the xy plane under the influence of the two-dimensional harmonic oscillator potential

(a) Construct the ground state wave function, Ψ₀(x,y), and write down its energy. Do the same for the (degenerate) first excited states.
(b) Now imagine that we turn on a weak magnetic field of magnitude B₀ pointing in the z-direction,so that (to first order in ) the Hamiltonian acquires an extra term

Treating this as a perturbation, find the first-order corrections to the energies of the ground state and first excited states.

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V (x, y) = √mw² (x² + y²).