Time-dependence of wave functions and the calculation of transition intensities

The standard formalism of the perturbation theory for time-dependent perturbations follows from the assumption that the exact solution of the unperturbed time-independent problem is known. The consequences of this assumption are analyzed. Particular attention is given to the methods used for the evaluation of transition intensities. It is shown that the traditional intensity formula in most cases violates the assumptions underlying its derivation. It is shown that for the given ansatz concerning the form of the approximate wave function, the transition intensities should be determined from the variation treatment of the corresponding time-dependent problem. The wave functions of both states involved in the transition should be given the same amount of variation flexibility. This condition is satisfied if the transition intensity expression follows from the complete timedependent perturbation treatment of the perturbed system.