Scattering Theory: Some Old and New Problems

• Main Author: Yafaev, Dmitri R. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.
• Edition: 1st ed. 2000.
• Series: Lecture Notes in Mathematics, 1735
• Subjects: Mathematical analysis.; Analysis (Mathematics).; Functional analysis.; Integral equations.; Partial differential equations.; Mathematical physics.; Analysis.; Functional Analysis.; Integral Equations.; Partial Differential Equations.; Theoretical, Mathematical and Computational Physics.

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, suc...

Table of Contents:

• Basic concepts
• Short-range interactions. asymptotic completeness
• Short-range interactions. Miscellaneous
• Long-range interactions. The scheme of smooth perturbations
• The generalized fourier transform
• Long-range matrix potentials
• A stationary representation
• The short-range case
• The long-range case
• The relative scattering matrix
• Setting the scattering problem
• Resolvent equations for three-particle systems
• Asymptotic completeness. A sketch of proof
• The scattering matrix and eigenfunctions for multiparticle systems
• New channels of scattering
• The heisenberg model
• Infinite obstacle scattering.