Asymptotically Outgoing and Incoming Spaces and Quantum Scattering

Abstract

The notion of outgoing and incoming spaces of Lax-Phillips [17] is generalized to asymptotically outgoing and incoming spaces. With this notion of asymptotically outgoing and incoming spaces, it is shown that the existence and asymptotic completeness of wave operators in quantum scattering theory is obtained by a slightly modified proof of Theorem 1.2 in [17].