Sinopsis
Explore how to uncover hidden structures from scattered waves. This book guides you through a rigorous approach to determine material properties from measured scattering data.
The work analyzes the problem of finding how electron density varies in a weakly ionized gas by using the scattering amplitude from a plane electromagnetic wave. It develops a framework that treats wave propagation with a scalar model and connects the inverse problem to integral equations, spectral weights, and scattering operators. Readers will see how different mathematical tools come together to address a physically motivated, three‑dimensional inverse scattering question.
Along with foundational conventions and notation, the text presents an integral transform theorem and the role of the spectral weight operator in linking data to the underlying kernel. It discusses how a scattering operator can encapsulate essential information and what conditions can guarantee unique recovery of the system’s kernel from partial knowledge of the scattering operator. The material is aimed at readers with interest in mathematical physics and applied analysis of wave phenomena.
- Understand the physical setup and the goal of determining a kernel from scattering data.
- Learn how integral equations, eigenfunctions, and transform theorems are used in inverse problems.
- Explore the role of the spectral weight operator and the scattering operator in reconstruction.
- See how uniqueness conditions are formulated and why they matter for recovery.
Ideal for readers of mathematical physics, applied analysis, and engineering disciplines that use wave scattering to probe materials.
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Reseña del editor
Excerpt from The Three-Dimensional Inverse Scattering Problem
The purpose of this paper is to put together in a concrete form the mathematical theory of an inverse scattering problem which was originally formulated in quantum mechanical terms but which is related to the problem of determining the variation of electron density in an ionized gas such as the earth's ionosphere by means of radio sounding experiments. The theory described here was developed by H. E. Moses and the present writer and was originally presented.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Excerpt from The Three-Dimensional Inverse Scattering Problem
The Three-Dimensional Inverse Scattering Problem was written by Irvin W. Kay. This is a 50 page book, containing 6645 words. Search Inside is enabled for this title.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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The Three-Dimensional Inverse Scattering Problem (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book presents a mathematical framework for understanding the inverse scattering problem as it pertains to the study of weakly ionized gases within an electromagnetic field. The scattering problem involves finding the properties of a medium by analyzing how it scatters electromagnetic waves. The inverse scattering problem is determining the medium's properties from the scattered waves. The author provides a detailed exploration of the theoretical underpinnings of the inverse scattering problem, offering a rigorous examination of relevant concepts such as integral transform theorems, spectral weight operators, and the scattering operator. The text also explores the conditions necessary for a unique solution to the inverse scattering problem and discusses the implications of these conditions for practical applications. Through its exploration of the inverse scattering problem, this book contributes to ongoing research in electromagnetism and plasma physics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781330149591_0
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The ThreeDimensional Inverse Scattering Problem Classic Reprint
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The Three-Dimensional Inverse Scattering Problem (Classic Reprint)
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Paperback. Condición: Brand New. 54 pages. 8.43x5.85x0.73 inches. This item is printed on demand. Nº de ref. del artículo: zk1330149599
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The Three-Dimensional Inverse Scattering Problem (Classic Reprint)
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ISBN 10: 1330149599
ISBN 13: 9781330149591
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Condición: Hervorragend. Zustand: Hervorragend | Seiten: 54 | Sprache: Englisch | Produktart: Bücher | Keine Beschreibung verfügbar. Nº de ref. del artículo: 25787064/1
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