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Scattering Theory: Some Old and New Problems (Lecture Notes in Mathematics)
Scattering Theory: Some Old and New Problems (Lecture Notes in Mathematics)
Date: 13 April 2011, 03:43

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Product Description: Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrodinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. We construct also potentials for which asymptotic completeness is violated. This corresponds to a new class of asymptotic solutions of the time-dependent Schrodinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.

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