A nonrelativistic hydrogen atom, with a spinless clectron, is placed in an electric field E in the z dircction and a magnetic field H in the r direction. The effect of the two ficlds on the energy levcls are comparable. (a) If the atom is in a state with n, the principal quantun number, equal to two, state which matrix cleinents in the first-order perturbation calculation of the energy shifts are zero. (b) Now obtain an cquation for the encergy shifts; once you have the determinantal cquation you ced not go through the algebra of cvaluating the determinlaut. Do not inscrt the precise forms of the radial wave func- tions; cxpress your results in terms of matrix clements of r" (wherc n is an appropriate power) between radial wave functions. (lz t ily)|e, in) = /{(l7 m) (l ±1m + 1)}|e, m± 1) .

A nonrelativistic hydrogen atom, with a spinless clectron, is placed in an electric field E in the z dircction and a magnetic field H in the r direction. The effect of the two ficlds on the energy levcls are comparable. (a) If the atom is in a state with n, the principal quantun number, equal to two, state which matrix cleinents in the first-order perturbation calculation of the energy shifts are zero. (b) Now obtain an cquation for the encergy shifts; once you have the determinantal cquation you ced not go through the algebra of cvaluating the determinlaut. Do not inscrt the precise forms of the radial wave func- tions; cxpress your results in terms of matrix clements of r" (wherc n is an appropriate power) between radial wave functions. (lz t ily)|e, in) = /{(l7 m) (l ±1m + 1)}|e, m± 1) .