Quantum Theory of Scattering
Quantum Theory of Scattering

Author: Ta-you Wu

Publisher: Courier Corporation

Published: 2014-01-15

Total Pages: 530

ISBN-13: 0486320693

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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.

Principles of Quantum Scattering Theory
Principles of Quantum Scattering Theory

Author: Dzevad Belkic

Publisher: CRC Press

Published: 2020-01-15

Total Pages: 402

ISBN-13: 9781420033649

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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.

Scattering Theory of Classical and Quantum N-Particle Systems
Scattering Theory of Classical and Quantum N-Particle Systems

Author: Jan Derezinski

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 448

ISBN-13: 3662034034

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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.

Scattering Theory
Scattering Theory

Author: John R. Taylor

Publisher: Courier Corporation

Published: 2012-05-23

Total Pages: 498

ISBN-13: 0486142078

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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.

Scattering Theory of Waves and Particles
Scattering Theory of Waves and Particles

Author: R.G. Newton

Publisher: Springer Science & Business Media

Published: 2013-11-27

Total Pages: 758

ISBN-13: 3642881289

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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.

Scattering Theory
Scattering Theory

Author: Harald Friedrich

Publisher: Springer

Published: 2015-11-20

Total Pages: 293

ISBN-13: 3662485265

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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.

Scattering Matrix Approach to Non-stationary Quantum Transport
Scattering Matrix Approach to Non-stationary Quantum Transport

Author: Michael V. Moskalets

Publisher: World Scientific

Published: 2012

Total Pages: 297

ISBN-13: 1848168349

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The aim of this book is to introduce the basic elements of the scattering matrix approach to transport phenomena in dynamical quantum systems of non-interacting electrons. This approach permits a physically clear and transparent description of transport processes in dynamical mesoscopic systems, promising basic elements of solid-state devices for quantum information processing. One of the key effects, the quantum pump effect, is considered in detail. In addition, the theory for the recently implemented new dynamical source ? injecting electrons with time delay much larger than an electron coherence time ? is offered. This theory provides a simple description of quantum circuits with such a single-particle source and shows in an unambiguous way that the tunability inherent to the dynamical systems (in contrast to the stationary ones) leads to a number of unexpected but fundamental effects.

Quantum Inverse Scattering Method and Correlation Functions
Quantum Inverse Scattering Method and Correlation Functions

Author: V. E. Korepin

Publisher: Cambridge University Press

Published: 1997-03-06

Total Pages: 582

ISBN-13: 9780521586467

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The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Go rdon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians.The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results.The book will be essential reading for all mathematical physicists working in field theory and statistical physics.

Variational Methods in Electron-Atom Scattering Theory
Variational Methods in Electron-Atom Scattering Theory

Author: Robert K. Nesbet

Publisher: Springer Science & Business Media

Published: 2013-11-21

Total Pages: 234

ISBN-13: 1468484311

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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.