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Author : Michael Reed
Publisher : Academic Press
ISBN 13 :
Total Pages : 488 pages
Book Rating : 4.3/5 (91 download)
Download or read book III: Scattering Theory written by Michael Reed and published by Academic Press. This book was released on 1979-04-28 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 3.
Author : R.G. Newton
Publisher : Springer Science & Business Media
ISBN 13 : 3642881289
Total Pages : 758 pages
Book Rating : 4.6/5 (428 download)
Download or read book Scattering Theory of Waves and Particles written by R.G. Newton and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much progress has been made in scattering theory since the publication of the first edition of this book fifteen years ago, and it is time to update it. Needless to say, it was impossible to incorporate all areas of new develop ment. Since among the newer books on scattering theory there are three excellent volumes that treat the subject from a much more abstract mathe matical point of view (Lax and Phillips on electromagnetic scattering, Amrein, Jauch and Sinha, and Reed and Simon on quantum scattering), I have refrained from adding material concerning the abundant new mathe matical results on time-dependent formulations of scattering theory. The only exception is Dollard's beautiful "scattering into cones" method that connects the physically intuitive and mathematically clean wave-packet description to experimentally accessible scattering rates in a much more satisfactory manner than the older procedure. Areas that have been substantially augmented are the analysis of the three-dimensional Schrodinger equation for non central potentials (in Chapter 10), the general approach to multiparticle reaction theory (in Chapter 16), the specific treatment of three-particle scattering (in Chapter 17), and inverse scattering (in Chapter 20). The additions to Chapter 16 include an introduction to the two-Hilbert space approach, as well as a derivation of general scattering-rate formulas. Chapter 17 now contains a survey of various approaches to the solution of three-particle problems, as well as a discussion of the Efimov effect.
Author : Dmitri R. Yafaev
Publisher : Springer
ISBN 13 : 3540451706
Total Pages : 185 pages
Book Rating : 4.5/5 (44 download)
Download or read book Scattering Theory: Some Old and New Problems written by Dmitri R. Yafaev and published by Springer. This book was released on 2007-05-06 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.
Author : Jan Derezinski
Publisher : Springer Science & Business Media
ISBN 13 : 3662034034
Total Pages : 448 pages
Book Rating : 4.6/5 (62 download)
Download or read book Scattering Theory of Classical and Quantum N-Particle Systems written by Jan Derezinski and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Dzevad Belkic
Publisher : CRC Press
ISBN 13 : 9781420033649
Total Pages : 402 pages
Book Rating : 4.0/5 (336 download)
Download or read book Principles of Quantum Scattering Theory written by Dzevad Belkic and published by CRC Press. This book was released on 2020-01-15 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering is one of the most powerful methods used to study the structure of matter, and many of the most important breakthroughs in physics have been made by means of scattering. Nearly a century has passed since the first investigations in this field, and the work undertaken since then has resulted in a rich literature encompassing both experimental and theoretical results. In scattering, one customarily studies collisions among nuclear, sub-nuclear, atomic or molecular particles, and as these are intrinsically quantum systems, it is logical that quantum mechanics is used as the basis for modern scattering theory. In Principles of Quantum Scattering Theory, the author judiciously combines physical intuition and mathematical rigour to present various selected principles of quantum scattering theory. As always in physics, experiment should be used to ultimately validate physical and mathematical modelling, and the author presents a number of exemplary illustrations, comparing theoretical and experimental cross sections in a selection of major inelastic ion-atom collisions at high non-relativistic energies. Quantum scattering theory, one of the most beautiful theories in physics, is also very rich in mathematics. Principles of Quantum Scattering Theory is intended primarily for graduate physics students, but also for non-specialist physicists for whom the clarity of exposition should aid comprehension of these mathematical complexities.
Author : Baumgärtel
Publisher : Birkhäuser
ISBN 13 : 3034854404
Total Pages : 448 pages
Book Rating : 4.0/5 (348 download)
Download or read book Mathematical Scattering Theory written by Baumgärtel and published by Birkhäuser. This book was released on 2013-12-11 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Andrey V. Osipov
Publisher : John Wiley & Sons
ISBN 13 : 1119293294
Total Pages : 824 pages
Book Rating : 4.1/5 (192 download)
Download or read book Modern Electromagnetic Scattering Theory with Applications written by Andrey V. Osipov and published by John Wiley & Sons. This book was released on 2017-01-31 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book gives fundamental knowledge about scattering and diffraction of electromagnetic waves and fills the gap between general electromagnetic theory courses and collections of engineering formulas. The book is a tutorial for advanced students learning the mathematics and physics of electromagnetic scattering and curious to know how engineering concepts and techniques relate to the foundations of electromagnetics
Author : Calvin H. Wilcox
Publisher : Springer Science & Business Media
ISBN 13 : 1461211301
Total Pages : 172 pages
Book Rating : 4.4/5 (612 download)
Download or read book Scattering Theory for Diffraction Gratings written by Calvin H. Wilcox and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Z.S. Agranovich
Publisher : Courier Dover Publications
ISBN 13 : 0486842495
Total Pages : 307 pages
Book Rating : 4.4/5 (868 download)
Download or read book The Inverse Problem of Scattering Theory written by Z.S. Agranovich and published by Courier Dover Publications. This book was released on 2020-05-21 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph by two Soviet experts in mathematical physics was a major contribution to inverse scattering theory. The two-part treatment examines the boundary-value problem with and without singularities. 1963 edition.
Author : Richard B. Melrose
Publisher : Cambridge University Press
ISBN 13 : 9780521498104
Total Pages : 134 pages
Book Rating : 4.4/5 (981 download)
Download or read book Geometric Scattering Theory written by Richard B. Melrose and published by Cambridge University Press. This book was released on 1995-07-28 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are intended as a non-technical overview of scattering theory.
Author : Ta-you Wu
Publisher : Courier Corporation
ISBN 13 : 0486320693
Total Pages : 530 pages
Book Rating : 4.4/5 (863 download)
Download or read book Quantum Theory of Scattering written by Ta-you Wu and published by Courier Corporation. This book was released on 2014-01-15 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume addresses the broad formal aspects and applications of the quantum theory of scattering in atomic and nuclear collisions. An encyclopedic source of pioneering work, it serves as a text for students and a reference for professionals in the fields of chemistry, physics, and astrophysics. The self-contained treatment begins with the general theory of scattering of a particle by a central field. Subsequent chapters explore particle scattering by a non-central field, collisions between composite particles, the time-dependent theory of scattering, and nuclear reactions. An examination of dispersion relations concludes the text. Numerous graphs, tables, and footnotes illuminate each chapter, in addition to helpful appendixes and bibliographies.
Author : Semyon Dyatlov
Publisher : American Mathematical Soc.
ISBN 13 : 147044366X
Total Pages : 634 pages
Book Rating : 4.4/5 (74 download)
Download or read book Mathematical Theory of Scattering Resonances written by Semyon Dyatlov and published by American Mathematical Soc.. This book was released on 2019-09-10 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
Author : A. G. Sitenko
Publisher : Elsevier
ISBN 13 : 1483186822
Total Pages : 280 pages
Book Rating : 4.4/5 (831 download)
Download or read book Lectures in Scattering Theory written by A. G. Sitenko and published by Elsevier. This book was released on 2013-10-22 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures in Scattering Theory discusses problems in quantum mechanics and the principles of the non-relativistic theory of potential scattering. This book describes in detail the properties of the scattering matrix and its connection with physically observable quantities. This text presents a stationary formulation of the scattering problem and the wave functions of a particle found in an external field. This book also examines the analytic properties of the scattering matrix, dispersion relations, complex angular moments, as well as the separable representation of the scattering amplitude. The text also explains the method of factorizing the potential and the two-particle scattering amplitude, based on the Hilbert-Schmidt theorem for symmetric integral equations. In investigating the problem of scattering in a three-particle system, this book notes that the inapplicability of the Lippman-Schwinger equations can be fixed by appropriately re-arranging the equations. Faddeev equations are the new equations formed after such re-arrangements. This book also cites, as an example, the scattering of a spin-1/2 particle by a spinless particle (such as the scattering of a nucleon by a spinless nucleus). This text is suitable for students and professors dealing with quantum mechanics, theoretical nuclear physics, or other fields of advanced physics.
Author : Harald Friedrich
Publisher : Springer
ISBN 13 : 3662485265
Total Pages : 287 pages
Book Rating : 4.6/5 (624 download)
Download or read book Scattering Theory written by Harald Friedrich and published by Springer. This book was released on 2015-11-20 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is kept as low as at all possible and deeper questions related to the mathematical foundations of scattering theory are passed by. It should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. The book is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.
Author : John R. Taylor
Publisher : Courier Corporation
ISBN 13 : 0486142078
Total Pages : 512 pages
Book Rating : 4.4/5 (861 download)
Download or read book Scattering Theory written by John R. Taylor and published by Courier Corporation. This book was released on 2012-05-23 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text, intended for any student of physics who requires a thorough grounding in the quantum theory of nonrelativistic scattering, emphasizes the time-dependent approach. 1983 edition.
Author : Johannes M. Henn
Publisher : Springer
ISBN 13 : 3642540228
Total Pages : 195 pages
Book Rating : 4.6/5 (425 download)
Download or read book Scattering Amplitudes in Gauge Theories written by Johannes M. Henn and published by Springer. This book was released on 2014-02-07 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material present ed in the main text.
Author : Robert K. Nesbet
Publisher : Springer Science & Business Media
ISBN 13 : 1468484311
Total Pages : 234 pages
Book Rating : 4.4/5 (684 download)
Download or read book Variational Methods in Electron-Atom Scattering Theory written by Robert K. Nesbet and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The investigation of scattering phenomena is a major theme of modern physics. A scattered particle provides a dynamical probe of the target system. The practical problem of interest here is the scattering of a low energy electron by an N-electron atom. It has been difficult in this area of study to achieve theoretical results that are even qualitatively correct, yet quantitative accuracy is often needed as an adjunct to experiment. The present book describes a quantitative theoretical method, or class of methods, that has been applied effectively to this problem. Quantum mechanical theory relevant to the scattering of an electron by an N-electron atom, which may gain or lose energy in the process, is summarized in Chapter 1. The variational theory itself is presented in Chapter 2, both as currently used and in forms that may facilitate future applications. The theory of multichannel resonance and threshold effects, which provide a rich structure to observed electron-atom scattering data, is presented in Chapter 3. Practical details of the computational implementation of the variational theory are given in Chapter 4. Chapters 5 and 6 summarize recent appli cations of the variational theory to problems of experimental interest, with many examples of the successful interpretation of complex structural fea tures observed in scattering experiments, and of the quantitative prediction of details of electron-atom scattering phenomena.
