JournalsprimsVol. 41, No. 1pp. 73–111

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
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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.

Cite this article

Serge Richard, Spectral and Scattering Theory for Schrödinger Operators with Cartesian Anisotropy. Publ. Res. Inst. Math. Sci. 41 (2005), no. 1, pp. 73–111

DOI 10.2977/PRIMS/1145475405