Strong-field approximation for the Schrödinger equation

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Abstract
A perturbation series is derived for the Schrödinger equation where the perturbation is permitted to go to ∞. Such an asymptotic series can be obtained in a representation where the time evolution of the states is due to the unperturbed part of the Hamiltonian of the problem and the time evolution of the observables is determined by the perturbation, contrary to the interaction picture. The equivalence between the series given by such a picture, and an asymptotic perturbation scheme is given. The method is applied to a spin-1/2 particle in a two-component magnetic field, one component of which, considered as a perturbation, can be time varying. Choosing a constant perturbation we show the equivalence between the exact solution and the approximate one when a component of the magnetic field is much larger than the other. In this case the limit t→∞ cannot be taken, as mixed-secular terms appear in the asymptotic series. Taking a linear time-varying dependence for a component of the magnetic field, we get a nonanalytic asymptotic series.

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