Iii Scattering Theory
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Iii Scattering Theory
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Author : Michael Reed
language : en
Publisher: Academic Press
Release Date : 1979-04-28
Iii Scattering Theory written by Michael Reed and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-04-28 with Mathematics categories.
Volume 3.
Scattering Theory Of Waves And Particles
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Author : R.G. Newton
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Scattering Theory Of Waves And Particles written by R.G. Newton 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 2013-11-27 with Science categories.
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.
Iii Scattering Theory
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Author : Michael Reed
language : en
Publisher: Elsevier
Release Date : 1979-05-29
Iii Scattering Theory written by Michael Reed and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-05-29 with Science categories.
Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second, one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example, in x-ray crystallography (which led to the discovery of DNA), tomography, and the detection of underwater objects by sonar, the underlying dynamics is well understood. What one would like to construct are correspondences that link, via the dynamics, the position, shape, and internal structure of the object to the scattering data. Ideally, the correspondence should be an explicit formula which allows one to reconstruct, at least approximately, the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton, had he bothered to ask the right question, its calculation is generally attributed to Rutherford more than two hundred years later. Of course, Rutherford's calculation was in connection with the first experiment in nuclear physics.
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.
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.
Multiple Scattering Theory
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Author : J. S. Faulkner
language : en
Publisher:
Release Date : 2018
Multiple Scattering Theory written by J. S. Faulkner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Energy-band theory of solids categories.
"In 1947, it was discovered that multiple scattering theory can be used to solve the Schrèodinger equation for the stationary states of electrons in a solid. Written by experts in the field, Dr. J S Faulkner, G M Stocks, and Yang Wang, this book collates the results of numerous studies in the field of multiple scattering theory and provides a comprehensive, systematic approach to MSTs." -- Prové de l'editor.
Scattering Theory
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Author : Alekseĭ Grigorʹevich Sitenko
language : en
Publisher: Springer
Release Date : 1991-01-21
Scattering Theory written by Alekseĭ Grigorʹevich Sitenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-21 with Computers categories.
This book is based on the course in theoretical nuclear physics that has been given by the author for some years at the T. G. Shevchenko Kiev State University. This version is supplemented and revised to include new results obtained after 1971 and 1975 when the first and second editions were published. This text is intended as an introduction to the nonrelativistic theory of po tential scattering. The analysis is based on the scattering matrix concept where the relationship between the scattering matrix and observable physical quantities is considered. The stationary formulation of the scattering problem is presented; particle wave functions in the external field are obtained. A formulation of the optical theorem is given as well as a discussion on time inversion and the reci procity theorem. Analytic properties of the scattering matrix, dispersion relations, and complex moments are analyzed. The dispersion relations for an arbitrary di rection scattering amplitude are proven, and analytic properties of the amplitude in the plane of the complex cosine of the scattering angle are studied in detail.
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 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.
Principles Of Quantum Scattering Theory
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Author : Dzevad Belkic
language : en
Publisher: CRC Press
Release Date : 2020-01-15
Principles Of Quantum Scattering Theory written by Dzevad Belkic and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-15 with Science categories.
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.