Ap-orbital electron characterized by |n, l = l, m = ±1,0) (ignore spin) is subjected to a potential

(a) Obtain the "correct" zeroth-order energy eigenstates that diagonalize the perturbation. You need not evaluate the energy shifts in detail, but show that the original threefold degeneracy is now completely removed.

(b) Because V is invariant under time reversal and because there is no longer any degeneracy, we expect each of the energy eigenstates obtained in (a) to go into itself (up to a phase factor or sign) under time reversal. Check this point explicitly.

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V = λ(x² - y²) (λ = constant).