Existence of the Møller wave operators in quantum scattering theory

Abstract

Existence of the wave operators of quantum mechanical scattering theory is established. The Hamiltonians are constant coefficient partial differential operators and perturbations of them by variable coefficient linear partial differential operators. The coefficients may be short range in the usual sense but they may also be oscillating. The problem of establishing existence is reduced to that of approximating solutions of a certain partial differential equations on cones in phase space. The proof is based on a refinement of Cook's argument.