The nuclear method in potential scattering theory

The perturbation of a Schrodinger 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.