Direct and Inverse Scattering for the Matrix Schrödinger Equation
Authors: Aktosun, Tuncay, Weder, Ricardo
Free Preview- -Presents a complete and detailed matrix Marchenko method with general boundary conditions
- -Illustrates a comprehensive treatment of scattering theory through explicit examples
- -Indicates how the inverse problem should be posed and reveals how the existing formulation is problematic unless the boundary condition is specified as part of the scattering data
- -Investigates existence, uniqueness, and construction aspects of scattering and inverse scattering problems
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- About this book
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Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems.
The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set.
- Table of contents (6 chapters)
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Introduction
Pages 1-17
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The Matrix Schrödinger Equation and the Characterization of the Scattering Data
Pages 19-47
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Direct Scattering I
Pages 49-260
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Direct Scattering II
Pages 261-337
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Inverse Scattering
Pages 339-484
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Table of contents (6 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Direct and Inverse Scattering for the Matrix Schrödinger Equation
- Authors
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- Tuncay Aktosun
- Ricardo Weder
- Series Title
- Applied Mathematical Sciences
- Series Volume
- 203
- Copyright
- 2021
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-38431-9
- DOI
- 10.1007/978-3-030-38431-9
- Hardcover ISBN
- 978-3-030-38430-2
- Series ISSN
- 0066-5452
- Edition Number
- 1
- Number of Pages
- XIII, 624
- Number of Illustrations
- 1 b/w illustrations
- Topics
