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International Journal of Mathematics and Mathematical Sciences
Volume 15, Issue 1, Pages 175-182
http://dx.doi.org/10.1155/S016117129200019X

Long range scattering with Stark effect and almost periodic potentials

Denis A. W. White

Department of Mathematics, University of Toledo, Toledo, OH 43606, USA

Received 3 December 1990; Revised 20 August 1991

Copyright © 1992 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Spectral and scattering theory is discussed for the Stark effect Hamiltonians H0=−(1/2)Δ−x1 and H=H0+V where V is a long range perturbation. Most significantly, in one dimension, and for V consisting of a slowly decaying term and an almost periodic term, the two Hilbert space wave operators (of Isozaki and Kitada) are shown to exist and be complete by Enss's time dependent method.