Completeness for sparse potential scattering

The present paper is devoted to the scattering theory of a class of continuum Schrödinger operators with deterministic sparse potentials. We first establish the limiting absorption principle for both modified free resolvents and modified perturbed resolvents. This actually is a weak form of the clas...

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Bibliographic Details
Published in:Journal of mathematical physics 2014-01, Vol.55 (1), p.12108
Main Author: Shen, Zhongwei
Format: Article
Language:English
Subjects:
ABSORPTION
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Completeness
Constraining
Operators (mathematics)
Physics
POTENTIAL SCATTERING
POTENTIALS
Scattering
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Summary:The present paper is devoted to the scattering theory of a class of continuum Schrödinger operators with deterministic sparse potentials. We first establish the limiting absorption principle for both modified free resolvents and modified perturbed resolvents. This actually is a weak form of the classical limiting absorption principle. We then prove the existence and completeness of local wave operators, which, in particular, imply the existence of wave operators. Under additional assumptions on the sparse potential, we prove the completeness of wave operators. In the context of continuum Schrödinger operators with sparse potentials, this paper gives the first proof of the completeness of wave operators.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4862192