Consider a particle in a two-dimensional potential
V₀ = { 0, for 0, ≤ x ≤ L, 0 ≤ y ≤ L
{[infinity], otherwise
Write the energy eigenfunctions for the ground state and the first excited state. We now add a time-independent perturbation of the form
V₁ = { λxy, for 0 ,≤ x ≤ L, 0 ≤ y ≤ L
{ 0, otherwise
Obtain the zeroth-order energy eigenfunctions and the first-order energy shifts for the ground state and the first excited state.