03-69 Serge Richard
Spectral and Scattering Theory for Schrodinger Operators with Cartesian Anisotropy (812K, PostScript) Feb 21, 03
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Abstract. We study the spectral and scattering theory of some n-dimensional anisotropic Schrodinger 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.

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