Spectral and Scattering Theory for Schrödinger Operators with Cartesian Anisotropy | Zendy

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Spectral and Scattering Theory for Schrödinger Operators with Cartesian Anisotropy

Author(s) -

Serge Richard

Publication year - 2005

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1145475405

Subject(s) - cartesian coordinate system , mathematics , anisotropy , scattering , spectral theory , pseudodifferential operators , schrödinger's cat , mathematical analysis , mathematical physics , pure mathematics , calculus (dental) , quantum mechanics , geometry , physics , hilbert space , medicine , dentistry

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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