Suppose we put a delta-function bump in the center of the infinite square well:...

Suppose we put a delta-function bump in the center of the infinite square well:

where α is a constant.

(a) Find the first-order correction to the allowed energies. Explain why the energies are not perturbed for even n.

(b) Find the first three nonzero terms in the expansion (Equation 6.13) of the correction to the ground state, .