Inverse Problems in Quantum Scattering Theory (Theoretical and Mathematical Physics)

Chadan, Khosrow; Sabatier, Pierre C.

ISBN 10: 3540187316 / ISBN 13: 9783540187318

Editore: Springer, 1989

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Titolo: Inverse Problems in Quantum Scattering ...

Casa editrice: Springer

Data di pubblicazione: 1989

Legatura: Hardcover

Condizione: Like New

Edizione: seconda edizione

Tipologia articolo: book

Descrizione articolo

Riassunto:

The physical importance of inverse problems in quantum scattering theory is clear since all the information we can obtain on nuclear, particle, and subparticle physics is gathered from scattering experiments. Exact and approximate methods of investigating scattering theory, inverse radial problems at fixed energy, inverse one-dimensional problems, inverse three-dimensional problems, and construction of the scattering amplitude from the cross section are presented. The methods often apply to other fields, e. g. applied mathematics and geophysics. The book will therefore be of interest to theoretical and mathematical physicists, nuclear particle physicists, and chemical physicists. For the second edition the chapters on one-dimensional and three-dimensional scattering problems have been rewritten and considerably expanded. Furthermore, two new chapters on spectral problems and on numerical aspects have been added; in the sections on classical methods the comments and references have been updated.

Contenuti:

Contents: Some Results from Scattering Theory.- Bound States - Eigenfunction Expansions.- The Gel'fand-Levitan-Jost-Kohn Method.- Applications of the Gel'fand-Levitan Equation.- The Marchenko Method.- Examples.- Special Classes of Potentials.- Nonlocal Separable Interactions.- Miscellaneous Approaches to the Inverse Problems at Fixed l.- Scattering Amplitudes from Elastic Cross Sections.- Potentials from the Scattering Amplitude at Fixed Energy: General Equation and Mathematical Tools.- Potentials from the Scattering Amplitude at Fixed Energy: Matrix Methods.- Potentials from the Scattering Amplitude at Fixed Energy: Operator Methods.- The Three-Dimensional Inverse Problem.- Miscellaneous Approaches to Inverse Problems at Fixed Energy.- Approximate Methods.- Inverse Problems in One Dimension.- Problems Connected with Discrete Spectra.- Numerical Problem.- Reference List.- Subject Index.