Download or read book Dispersion Decay and Scattering Theory written by Alexander Komech and published by John Wiley & Sons. This book was released on 2014-08-21 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A simplified, yet rigorous treatment of scattering theory methods and their applications Dispersion Decay and Scattering Theory provides thorough, easy-to-understand guidance on the application of scattering theory methods to modern problems in mathematics, quantum physics, and mathematical physics. Introducing spectral methods with applications to dispersion time-decay and scattering theory, this book presents, for the first time, the Agmon-Jensen-Kato spectral theory for the Schr?dinger equation, extending the theory to the Klein-Gordon equation. The dispersion decay plays a crucial role in the modern application to asymptotic stability of solitons of nonlinear Schr?dinger and Klein-Gordon equations. The authors clearly explain the fundamental concepts and formulas of the Schr?dinger operators, discuss the basic properties of the Schr?dinger equation, and offer in-depth coverage of Agmon-Jensen-Kato theory of the dispersion decay in the weighted Sobolev norms. The book also details the application of dispersion decay to scattering and spectral theories, the scattering cross section, and the weighted energy decay for 3D Klein-Gordon and wave equations. Complete streamlined proofs for key areas of the Agmon-Jensen-Kato approach, such as the high-energy decay of the resolvent and the limiting absorption principle are also included. Dispersion Decay and Scattering Theory is a suitable book for courses on scattering theory, partial differential equations, and functional analysis at the graduate level. The book also serves as an excellent resource for researchers, professionals, and academics in the fields of mathematics, mathematical physics, and quantum physics who would like to better understand scattering theory and partial differential equations and gain problem-solving skills in diverse areas, from high-energy physics to wave propagation and hydrodynamics.
Download or read book Scattering Theory written by Alekseĭ Grigorʹevich Sitenko and published by Springer. This book was released on 1991-01-21 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Three particle Physics and Dispersion Relation Theory written by A. V. Anisovich and published by World Scientific. This book was released on 2013 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The necessity of describing three-nucleon and three-quark systems have led to a constant interest in the problem of three particles. The question of including relativistic effects appeared together with the consideration of the decay amplitude in the framework of the dispersion technique. The relativistic dispersion description of amplitudes always takes into account processes connected with the investigated reaction by the unitarity condition or by virtual transitions; in the case of three-particle processes they are, as a rule, those where other many-particle states and resonances are produced. The description of these interconnected reactions and ways of handling them is the main subject of the book.
Download or read book Collision Theory written by Marvin L. Goldberger and published by Courier Corporation. This book was released on 2004-01-01 with total page 930 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic description of the basic principles of collision theory, this graduate-level text presents a detailed examination of scattering processes and formal scattering theory, the two-body problem with central forces, scattering by noncentral forces, lifetime and decay of virtual states, an introduction to dispersion theory, and more. 1964 edition.
Download or read book PDE s dispersion scattering theory and control theory written by Kaïs Ammari and published by . This book was released on 2017 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dispersion Relations for Hyperon Decay written by Edward Richard McCliment and published by . This book was released on 1962 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conte t : Dispersion relations for yperon dec y The absorptive parts of the amplitude General considerations The rescatt ring t rm The b orn term The integral e uations Results Conclusions Relation with leptonic decays Application of time reversal invariance to decay amplitudes.
Download or read book Scattering Theory written by Peter D. Lax and published by . This book was released on 1967 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Dispersive Partial Differential Equations and Inverse Scattering written by Peter D. Miller and published by Springer Nature. This book was released on 2019-11-14 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures and invited papers from the Focus Program on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" held at the Fields Institute from July 31-August 18, 2017. The conference brought together researchers in completely integrable systems and PDE with the goal of advancing the understanding of qualitative and long-time behavior in dispersive nonlinear equations. The program included Percy Deift’s Coxeter lectures, which appear in this volume together with tutorial lectures given during the first week of the focus program. The research papers collected here include new results on the focusing nonlinear Schrödinger (NLS) equation, the massive Thirring model, and the Benjamin-Bona-Mahoney equation as dispersive PDE in one space dimension, as well as the Kadomtsev-Petviashvili II equation, the Zakharov-Kuznetsov equation, and the Gross-Pitaevskii equation as dispersive PDE in two space dimensions. The Focus Program coincided with the fiftieth anniversary of the discovery by Gardner, Greene, Kruskal and Miura that the Korteweg-de Vries (KdV) equation could be integrated by exploiting a remarkable connection between KdV and the spectral theory of Schrodinger's equation in one space dimension. This led to the discovery of a number of completely integrable models of dispersive wave propagation, including the cubic NLS equation, and the derivative NLS equation in one space dimension and the Davey-Stewartson, Kadomtsev-Petviashvili and Novikov-Veselov equations in two space dimensions. These models have been extensively studied and, in some cases, the inverse scattering theory has been put on rigorous footing. It has been used as a powerful analytical tool to study global well-posedness and elucidate asymptotic behavior of the solutions, including dispersion, soliton resolution, and semiclassical limits.
Download or read book Elementary Particle Physics and Scattering Theory written by Max Chrétien and published by . This book was released on 1970 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solitons and the Inverse Scattering Transform written by Mark J. Ablowitz and published by SIAM. This book was released on 2006-05-15 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.
Download or read book Scattering Theory of Waves and Particles written by Roger G. Newton and published by Courier Corporation. This book was released on 2002-01-01 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume crosses the boundaries of physics' traditional subdivisions to treat scattering theory within the context of classical electromagnetic radiation, classical particle mechanics, and quantum mechanics. Includes updates on developments in three-particle collisions, scattering by noncentral potentials, and inverse scattering problems. 1982 edition.
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 498 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.
Download or read book Weak Interactions and Topics in Dispersion Physics written by Christian Fronsdal and published by . This book was released on 1963 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scattering Theory written by Aleksei G. Sitenko and published by Springer. This book was released on 1991 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Coulomb Wave Scattering Theory and Dispersion Relations written by John Robert Rix and published by . This book was released on 1966 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
