Fourier Scattering Subspaces

Authors: Karl Gustafson

Publish Date: 1974

Volume: , Issue: , Pages: 277-285

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Abstract

In the literature of quantum mechanical scattering one finds that the scattering states are often being thought of as “the orthogonal complement of the bound states” or as “the outgoing states” or as “the asymptotic states” etc somewhat more precisely as the physically realizable evolutions “possessing incoming and outgoing asymptotic free states” or a little more precisely as evolutions whose initial values at t = 0 are in the range of a wave operator or operators eg in mathcalR + cap mathcalR + etc Recently there has been considerable interest in seeking a more fundamental understanding of scattering states in this paper we wish to show and to emphasize albeit in a brief and not yet complete manner the use of the Fourier theory as an essential ingredient in such investigations In particular we will obtain from a mathematical point of view some orderings of important types of scattering subspaces now under consideration

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