Consider the Stark effect (Problem 6.36) for the n = 3 states of hydrogen. There are initi...

Consider the Stark effect (Problem 6.36) for the n = 3 states of hydrogen. There are initially nine degenerate states, ψ31m(neglecting spin, as before), and we turn on an electric field in the z direction.

(a) Construct the 9 × 9 matrix representing the perturbing Hamiltonian. Partial answer: ⟨300|z|310⟩ = −3, ⟨310|z|320⟩ = −3, ⟨31±l|z|32±l⟩ = −(9/2)a.

(b) Find the eigenvalues, and their degeneracies.