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Inverse Problems in Scattering

An Introduction

  • Book
  • © 1993

Overview

Authors:
  1. G. M. L. Gladwell

    1. Department of Civil Engineering, University of Waterloo, Waterloo, Canada

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Part of the book series: Solid Mechanics and Its Applications (SMIA, volume 23)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
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  2. Some Simple Wave Phenomena

    • G. M. L. Gladwell
    Pages 1-53

  3. Layer-Peeling Methods for Discrete Inverse Problems

    • G. M. L. Gladwell
    Pages 55-89

  4. The Inversion of Discrete Systems Using Non-Causal Solutions

    • G. M. L. Gladwell
    Pages 91-122

  5. Waves in Non-Uniform Media

    • G. M. L. Gladwell
    Pages 123-145

  6. The Inversion of Continuous Systems Using Causal Solutions

    • G. M. L. Gladwell
    Pages 147-156

  7. Inversion of Continuous Systems Using Non-Causal Solutions

    • G. M. L. Gladwell
    Pages 157-187

  8. An Introduction to the Inverse Scattering Problem of Quantum Theory

    • G. M. L. Gladwell
    Pages 189-250

  9. The Schrödinger Equation on the Half Line

    • G. M. L. Gladwell
    Pages 251-287

  10. The Lebesque Integral

    • G. M. L. Gladwell
    Pages 289-318

  11. Inverse Scattering for the Schrödinger Equation

    • G. M. L. Gladwell
    Pages 319-344

  12. Back Matter

    Pages 345-366
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Keywords

About this book

Inverse Problems in Scattering exposes some of the mathematics which has been developed in attempts to solve the one-dimensional inverse scattering problem. Layered media are treated in Chapters 1--6 and quantum mechanical models in Chapters 7--10. Thus, Chapters 2 and 6 show the connections between matrix theory, Schur's lemma in complex analysis, the Levinson--Durbin algorithm, filter theory, moment problems and orthogonal polynomials. The chapters devoted to the simplest inverse scattering problems in quantum mechanics show how the Gel'fand--Levitan and Marchenko equations arose. The introduction to this problem is an excursion through the inverse problem related to a finite difference version of Schrödinger's equation. One of the basic problems in inverse quantum scattering is to determine what conditions must be imposed on the scattering data to ensure that they correspond to a regular potential, which involves Lebesque integrable functions, which are introduced in Chapter 9.

Authors and Affiliations

  • Department of Civil Engineering, University of Waterloo, Waterloo, Canada

    G. M. L. Gladwell

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