A Modification of the Dirac Time-Dependent Perturbation Theory
Abstract
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.
- Publication:
-
Proceedings of the Royal Society of London Series A
- Pub Date:
- August 1984
- DOI:
- 10.1098/rspa.1984.0083
- Bibcode:
- 1984RSPSA.394..345B