Scientific article

Spectral and Scattering Theory for Schrödinger Operators with Cartesian Anisotropy

ContributorsRichard, Serge
Publication date2005

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.

Citation (ISO format)
RICHARD, Serge. Spectral and Scattering Theory for Schrödinger Operators with Cartesian Anisotropy. In: Publications of the Research Institute for Mathematical Sciences, 2005, vol. 41, n° 1, p. 73–111. doi: 10.2977/PRIMS/1145475405
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Article (Published version)
ISSN of the journal0034-5318

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