Strongly perturbed quantum systems

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Abstract
We derive the integral form of the Schrödinger equation taking the Green function originating from the perturbation and prove the equivalence with the free representation. The equation is applied to a class of strong perturbing potentials of the form λw(x)g(t) with λ→∞. The method of stationary phase applied in this case gives the first terms of an asymptotic series for the probability amplitudes to find the system in one of the states of the unperturbed Hamiltonian, and these are shown to go to zero in the considered limit.