A hydrogen atom is placed in a (time-dependent) electric field E = E(t)k̂. Calculate all four matrix elements H'_ij of the perturbation Ĥ' = eEz between the ground state (n = 1) and the (quadruply degenerate) first excited states  (n = 2). Also show that  H'_ij = 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.