Inverse Problems in Scattering: An Introduction

✍ Scribed by G. M. L. Gladwell (auth.)

• Publisher: Springer Netherlands
• Year: 1993
• Tongue: English
• Leaves: 368
• Series: Solid Mechanics and its Applications 23
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-x
Some Simple Wave Phenomena....Pages 1-53
Layer-Peeling Methods for Discrete Inverse Problems....Pages 55-89
The Inversion of Discrete Systems Using Non-Causal Solutions....Pages 91-122
Waves in Non-Uniform Media....Pages 123-145
The Inversion of Continuous Systems Using Causal Solutions....Pages 147-156
Inversion of Continuous Systems Using Non-Causal Solutions....Pages 157-187
An Introduction to the Inverse Scattering Problem of Quantum Theory....Pages 189-250
The Schrödinger Equation on the Half Line....Pages 251-287
The Lebesque Integral....Pages 289-318
Inverse Scattering for the Schrödinger Equation....Pages 319-344
Back Matter....Pages 345-366

✦ Subjects

Theoretical, Mathematical and Computational Physics;Engineering, general