Suppose we perturb the infinite cubical well (Problem 4.2) by putting a delta function "bump" at the point (a/4,a/2,3a/4):
H′=a3V0δ(x−a/4)δ(y−a/2)δ(z−3a/4).
Find the first-order corrections to the energy of the ground state and the (triply degenerate) first excited states.