Stationary scattering theory for repulsive Hamiltonians

Abstract

In the present paper we discuss stationary scattering theory for repulsive Hamiltonians. We show the existence and completeness of stationary wave operators and unitarity of the scattering matrix. Moreover we completely characterize asymptotic behaviors of generalized eigenfunctions with minimal growth in terms of the scattering matrix. In our argument the radiation condition bounds for limiting resolvents play major roles. In fact, it is used to construct the stationary wave operators.