Applied Mathematical Sciences

Direct and Inverse Scattering for the Matrix Schrödinger Equation

Authors: Aktosun, Tuncay, Weder, Ricardo

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  • -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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eBook 46,00 €
89,99 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-38431-9
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Hardcover 57,19 €
114,39 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-38430-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
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About this book

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)

Table of contents (6 chapters)

Buy this book

eBook 46,00 €
89,99 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-38431-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 57,19 €
114,39 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-38430-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Direct and Inverse Scattering for the Matrix Schrödinger Equation
Authors
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