Overview
- 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
Part of the book series: Applied Mathematical Sciences (AMS, volume 203)
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Table of contents (6 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Direct and Inverse Scattering for the Matrix Schrödinger Equation
Authors: Tuncay Aktosun, Ricardo Weder
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-030-38431-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-38430-2Published: 19 May 2020
Softcover ISBN: 978-3-030-38433-3Published: 19 May 2021
eBook ISBN: 978-3-030-38431-9Published: 19 May 2020
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 1
Number of Pages: XIII, 624
Number of Illustrations: 1 b/w illustrations
Topics: Partial Differential Equations, Functional Analysis, Quantum Physics, Mathematical Physics