The change in energy levels in an atom due to the application of an external electric field is known as the Stark effect. The perturbation corresponding to a uniform static electric field of magnitude &, applied in the z-direction to a hydrogen atom, is H' = e&z = e&r cos 0. Use degenerate perturbation theory to calculate the effect on the four-fold degenerate n = 2 level of atomic hydrogen. The relevant unperturbed eigenfunctions are U200 = (87a;) 1 2ao exp (-r/2ao) , -1/2 r U211 = - (na3) sin 0 exp (ico ) exp (-r/2ao) , 8do U210 = (8na3) -1/2 r cos 0 exp (-r/2do) , 2ac -1/2 r U21-1 = (na) 8ao sin 0 exp (-i ) exp (-r/2ao)