JournalsprimsVol. 41 , No. 1DOI 10.2977/prims/1145475405

Spectral and Scattering Theory for Schrödinger Operators with Cartesian Anisotropy

  • Serge Richard

    Department of Theoretical Physics, Université de Genève
Spectral and Scattering Theory for Schrödinger Operators with Cartesian Anisotropy cover

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.