Mathematical Scattering Theory
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Mathematical Scattering Theory
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Author : D. R. Yafaev
language : en
Publisher: American Mathematical Soc.
Release Date : 1992-09-09
Mathematical Scattering Theory written by D. R. Yafaev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-09-09 with Mathematics categories.
Preliminary facts Basic concepts of scattering theory Further properties of the WO Scattering for relatively smooth perturbations The general setup in stationary scattering theory Scattering for perturbations of trace class type Properties of the scattering matrix (SM) The spectral shift function (SSF) and the trace formula
Mathematical Theory Of Scattering Resonances
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Author : Semyon Dyatlov
language : en
Publisher:
Release Date : 2019
Mathematical Theory Of Scattering Resonances written by Semyon Dyatlov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Frequencies of oscillating systems categories.
Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros.
A Qualitative Approach To Inverse Scattering Theory
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Author : Fioralba Cakoni
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-28
A Qualitative Approach To Inverse Scattering Theory written by Fioralba Cakoni and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-28 with Mathematics categories.
Inverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms for solving inverse scattering problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques. The limitations of these methods have led in recent years to an alternative approach to the inverse scattering problem which avoids the incorrect model assumptions inherent in the use of weak scattering approximations as well as the strong a priori information needed in order to implement nonlinear optimization techniques. These new methods come under the general title of qualitative methods in inverse scattering theory and seek to determine an approximation to the shape of the scattering object as well as estimates on its material properties without making any weak scattering assumption and using essentially no a priori information on the nature of the scattering object. This book is designed to be an introduction to this new approach in inverse scattering theory focusing on the use of sampling methods and transmission eigenvalues. In order to aid the reader coming from a discipline outside of mathematics we have included background material on functional analysis, Sobolev spaces, the theory of ill posed problems and certain topics in in the theory of entire functions of a complex variable. This book is an updated and expanded version of an earlier book by the authors published by Springer titled Qualitative Methods in Inverse Scattering Theory Review of Qualitative Methods in Inverse Scattering Theory All in all, the authors do exceptionally well in combining such a wide variety of mathematical material and in presenting it in a well-organized and easy-to-follow fashion. This text certainly complements the growing body of work in inverse scattering and should well suit both new researchers to the field as well as those who could benefit from such a nice codified collection of profitable results combined in one bound volume. SIAM Review, 2006
Mathematical Scattering Theory
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Author : Dmitriĭ Rauelʹevich Yafaev
language : en
Publisher: American Mathematical Society(RI)
Release Date : 1992
Mathematical Scattering Theory written by Dmitriĭ Rauelʹevich Yafaev and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Scattering theory presents an excellent example of interaction between different mathematical subjects: operator theory, measure theory, the theory of differential operators and equations, mathematical analysis, and applications of these areas to quantum mechanics . Because of the interplay of these fields, a deep understanding of scattering theory can lead to deep insights into the developing world of modern mathematics.
Scattering Theory For Diffraction Gratings
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Author : Calvin H. Wilcox
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Scattering Theory For Diffraction Gratings written by Calvin H. Wilcox and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The scattering of acoustic and electromagnetic waves by periodic sur faces plays a role in many areas of applied physics and engineering. Opti cal diffraction gratings date from the nineteenth century and are still widely used by spectroscopists. More recently, diffraction gratings have been used as coupling devices for optical waveguides. Trains of surface waves on the oceans are natural diffraction gratings which influence the scattering of electromagnetic waves and underwater sound. Similarly, the surface of a crystal acts as a diffraction grating for the scattering of atomic beams. This list of natural and artificial diffraction gratings could easily be extended. The purpose of this monograph is to develop from first principles a theory of the scattering of acoustic and electromagnetic waves by periodic surfaces. In physical terms, the scattering of both time-harmonic and transient fields is analyzed. The corresponding mathematical model leads to the study of boundary value problems for the Helmholtz and d'Alembert wave equations in plane domains bounded by periodic curves. In the formal ism adopted here these problems are intimately related to the spectral analysis of the Laplace operator, acting in a Hilbert space of functions defined in the domain adjacent to the grating.
Integral Equation Methods In Scattering Theory
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Author : David Colton
language : en
Publisher: SIAM
Release Date : 2013-11-15
Integral Equation Methods In Scattering Theory written by David Colton and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-15 with Mathematics categories.
This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.
Scattering Theory Of Classical And Quantum N Particle Systems
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Author : Jan Derezinski
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-06-05
Scattering Theory Of Classical And Quantum N Particle Systems written by Jan Derezinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-05 with Mathematics categories.
This monograph addresses researchers and students. It is a modern presentation of time-dependent methods for studying problems of scattering theory in the classical and quantum mechanics of N-particle systems. Particular attention is paid to long-range potentials. For a large class of interactions the existence of the asymptotic velocity and the asymptotic completeness of the wave operators is shown. The book is self-contained and explains in detail concepts that deepen the understanding. As a special feature of the book, the beautiful analogy between classical and quantum scattering theory (e.g., for N-body Hamiltonians) is presented with deep insight into the physical and mathematical problems.
Mathematical Scattering Theory
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Author : Baumgärtel
language : en
Publisher: Birkhäuser
Release Date : 2013-12-11
Mathematical Scattering Theory written by Baumgärtel and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Social Science categories.
The aim of this book is to give a systematic and self-contained presentation of the Mathematical Scattering Theory within the framework of operator theory in Hilbert space. The term Mathematical Scattering Theory denotes that theory which is on the one hand the common mathematical foundation of several physical scattering theories (scattering of quantum objects, of classical waves and particles) and on the other hand a branch of operator theory devoted to the study of the behavior of the continuous part of perturbed operators (some authors also use the term Abstract Scattering Theory). EBBential contributions to the development of this theory are due to K. FRIEDRICHS, J. CooK, T. KATo, J. M. JAuCH, S. T. KURODA, M.S. BmMAN, M.G. KREiN, L. D. FAD DEEV, R. LAVINE, W. 0. AMREIN, B. SIMoN, D. PEARSON, V. ENss, and others. It seems to the authors that the theory has now reached a sufficiently developed state that a self-contained presentation of the topic is justified.
Inverse Acoustic And Electromagnetic Scattering Theory
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Author : David Colton
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Inverse Acoustic And Electromagnetic Scattering Theory written by David Colton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
In the five years since the first edition of this book appeared, the field of in verse scattering theory has continued to grow and flourish. Hence, when the opportunity for a second edition presented itself, we were pleased to have the possibility of updating our monograph to take into account recent developments in the area. As in the first edition, we have been motivated by our own view of inverse scattering and have not attempted to include all of the many new directions in the field. However, we feel that this new edition represents a state of the art overview of the basic elements of the mathematical theory of acoustic and electromagnetic inverse scattering. In addition to making minor corrections and additional comments in the text and updating the references, we have added new sections on Newton's method for solving the inverse obstacle problem (Section 5.3), the spectral theory of the far field operator (Section 8.4), a proof of the uniqueness of the solution to the inverse medium problem for acoustic waves (Section 10.2) and a method for determining the support of an inhomogeneous medium from far field data by solving a linear integral equation of the first kind (Section 10.7). We hope that this second edition will attract new readers to the beautiful and intriguing field of inverse scattering.
Geometric Scattering Theory
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Author : Richard B. Melrose
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-28
Geometric Scattering Theory written by Richard B. Melrose and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-28 with Mathematics categories.
These lecture notes are intended as a non-technical overview of scattering theory.