A modification of the Dirac time-dependent perturbation theory

Within the framework of the method of variation of constants, time-dependent perturbation theory is presented in a form that naturally eliminates the undesirable 'secular' terms for a time-independent perturbation, permits an order-by-order calculation of the exact wavefunction for a 'resonant' harmonic perturbation and offers a simple route to establish the adiabatic hypothesis in quantum mechanics. The formulation rests on the introduction of a flexibility in the choice of the phase factors associated with the varying amplitudes, together with development of a perturbation procedure that closely resembles the Brillouin-Wigner formalism in the static case, and which exploits the flexibility of the phase factors at each order of the theory. (author)