Ahydrogen atom is placed in a (time-dependent) electric field e=e(t)k^. calculate all four matrix elements h′ij of the perturbation h^′=eez between the ground state (n=1) and the (quadruply degenerate) first excited states (n=2). also show that h′ii=0 for all five states.
note: there is only one integral to be done here, if you exploit oddness with respect to z; only one of the n=2 states is "accessible" from the ground state by a perturbation of this form, and therefore the system functions as a two-state configuration-assuming transitions to higher excited states can be ignored.