Inverse Problems in Scattering : An Introduction

Graham M. L. Gladwell

ISBN 10: 0792324781 / ISBN 13: 9780792324782

Published by Springer Netherlands, Springer, 1993

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9780792324782

Bibliographic Details

• Title: Inverse Problems in Scattering : An Introduction
• Publisher: Springer Netherlands, Springer
• Publication Date: 1993
• Language: English
• ISBN 10: 0792324781
• ISBN 13: 9780792324782
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 237W x 163H x 31D millimeters 237 millimeters width by 163 millimeters height by 31 millimeters depth
• Weight: 606 grams

About this title

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.