Spectral and scattering theory for Schrödinger operators with cartesian anisotropy

Abstract

We study the spectral and scattering theory of some n-dimensional anisotropic Schrödinger operators. The characteristic of the potentials is that they admit limits at infinity separately for each variable. We give a detailed analysis of the spectrum: the essential spectrum, the thresholds, a Mourre estimate, a limiting absorption principle and the absence of singularly continuous spectrum. Then the asymptotic completeness is proved and a precise description of the asymptotic states is obtained in terms of a suitable family of asymptotic operators. © 2005 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.