The nuclear method in potential scattering theory

The perturbation of a Schrödinger operator H₀ with an arbitrary bounded potential function q, decreasing sufficiently fast at infinity, is considered. With the aid of results of the nuclear theory, for the corresponding pair of Hamiltonians H₀, H=H₀+q, one establishes the existence and the completeness of the wave operators. Generalizations are given to a wider class of unperturbed operators H₀, and also to perturbations by firstorder differential operators. In addition, perturbations by integral operators of Fourier type are investigated.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 171, pp. 12–35, 1989.