The Inverse Problem of Scattering Theory

by Agranovich, Z. S.; Marchenko, V. A.

• ISBN13: 9780486842493
• ISBN10: 0486842495
• Format: Paperback
• Copyright: 2020-05-13
• Publisher: Dover Pubns

Summary

In mathematical physics, the inverse scattering problem determines the characteristics of an object based on how it scatters radiation or particles. The approach is the inverse of the "direct scattering problem," which investigates how particles are distributed based on characteristics of the scattering object. This monograph by two prominent Soviet authorities in mathematical physics was a major contribution to the literature in this field.
The two-part treatment begins by examining the boundary-value problem without singularities. Topics include particular solutions of the system without singularities, the spectrum and scattering matrix for the boundary-value problem without singularities, Parseval's equality, and the inverse problem. The second part addresses the boundary-value problem with singularities, exploring special transformation operators, spectral analysis, and reconstruction of the problem from scattering data. Helpful Appendixes supplement the text.
For advanced undergraduates and graduate students in physics and related fields.

Author Biography

Z. S. Agranovich was a Soviet scientist whose published works include many papers on condensed matter physics, materials science, and related fields.
V. A. Marchenko is a Soviet/Ukranian mathematician who has written widely about topics in mathematics and mathematical physics.

Table of Contents

Table of Contents:
Introduction
Part One: The Boundary-Value Problem  Without Singularities
I. Particular Solutions of the System Without Singularities
II. The Spectrum and Scattering Matrix for the Boundary-Value Problem
Without Singularities
III. The Fundamental Question
IV. Parseval's equality
V. The Inverse Problem
Part Two: The Boundary-Value Problem  With Singularities  
VI.  Special Transformation Operators
VII. Spectral Analysis of the Boundary-Value Problem With Singularities
VIII.  Reconstruction of the Singular Boundary-Value Problem From Its
Scattering Data
Appendix I: On the Characteristic Properties of the Scattering Data of the
Boundary-Value Problem Without Singularities.
Appendix II Refinement of Certain Inequalities
Bibliography
Index
Index of Notations