Download or read book Variable Phase Approach to Potential Scattering by F Calogero written by and published by Elsevier. This book was released on 1967-01-01 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Download or read book Variable Phase Approach to Potential Scattering written by F. Calogero and published by Elsevier Science & Technology. This book was released on 1967 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Download or read book New Series for Phase Shift in Potential Scattering written by S. Rosendorff and published by . This book was released on 1963 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Potential Scattering written by Vittorio De Alfaro and published by . This book was released on 1965 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combined Variable Phase R Matrix Approach to Scattering Problems written by John J. Matese and published by . This book was released on 1972 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Approximation Method for High energy Potential Scattering written by Jerome Johnson Tiemann and published by . This book was released on 1960 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scattering Two Volume Set written by E. R. Pike and published by Elsevier. This book was released on 2001-10-09 with total page 1831 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering is the collision of two objects that results in a change of trajectory and energy. For example, in particle physics, such as electrons, photons, or neutrons are "scattered off" of a target specimen, resulting in a different energy and direction. In the field of electromagnetism, scattering is the random diffusion of electromagnetic radiation from air masses is an aid in the long-range sending of radio signals over geographic obstacles such as mountains. This type of scattering, applied to the field of acoustics, is the spreading of sound in many directions due to irregularities in the transmission medium. Volume I of Scattering will be devoted to basic theoretical ideas, approximation methods, numerical techniques and mathematical modeling. Volume II will be concerned with basic experimental techniques, technological practices, and comparisons with relevant theoretical work including seismology, medical applications, meteorological phenomena and astronomy. This reference will be used by researchers and graduate students in physics, applied physics, biophysics, chemical physics, medical physics, acoustics, geosciences, optics, mathematics, and engineering. This is the first encyclopedic-range work on the topic of scattering theory in quantum mechanics, elastodynamics, acoustics, and electromagnetics. It serves as a comprehensive interdisciplinary presentation of scattering and inverse scattering theory and applications in a wide range of scientific fields, with an emphasis, and details, up-to-date developments. Scattering also places an emphasis on the problems that are still in active current research. The first interdisciplinary reference source on scattering to gather all world expertise in this technique Covers the major aspects of scattering in a common language, helping to widening the knowledge of researchers across disciplines The list of editors, associate editors and contributors reads like an international Who's Who in the interdisciplinary field of scattering
Download or read book Direct and Inverse Problems written by Boris N. Zakhariev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapid progress in quantum theory brings us new important results which are often not immediately clear to all who need them. But fortunately, this is also followed by simplifications and unifications of our previous concepts. The inverse problem method ("The most beautiful idea of the XX-th century" - Zakharov et aI., 1980) has just both these aspects. It is rather astonishing that it took 50 years after the foundation of quantum mechanics for the creation of the "pictures" showing the direct connection of obser vables with interactions. Recently, illustrations of this type began to appear in the literature (e. g., how potentials are deformed with thc shift of one energy level or change of some resonance reduced width). Although they are transparent to those studying the quantum world and can be included within the necessary elements of quantum literacy, they are still largely unknown even to many specialists. For the first time, the most interesting of these pictures enriching our quantum intuition are col lected here and placed at your disposal. The readers of this monograph have the advantage of getting the latest information which became available after the publication of the Russian edition. It has been incor porated here in the simplest presentation possible. For example, new sections con cerning exactly solvable models, including the multi-channel, multi-dimensional ones and with time dependent potentials have been added. The first attempts in solving the three-body inverse problem are also mentioned.
Download or read book Theory of Molecular Collisions written by Gabriel G. Balint-Kurti and published by Royal Society of Chemistry. This book was released on 2015-07-03 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost 100 years have passed since Trautz and Lewis put forward their collision theory of molecular processes. Today, knowledge of molecular collisions forms a key part of predicting and understanding chemical reactions. This book begins by setting out the classical and quantum theories of atom-atom collisions. Experimentally observable aspects of the scattering processes; their relationship to reaction rate constants and the experimental methods used to determine them are described. The quantum mechanical theory of reactive scattering is presented and related to experimental observables. The role of lasers in the measurement and analysis of reactive molecular collisions is also discussed. Written with postgraduates and newcomers to the field in mind, mathematics is kept to a minimum, and readers are guided to appendices and further reading to gain a deeper understanding of the mathematics involved.
Download or read book Inverse and Algebraic Quantum Scattering Theory written by Barnabas Apagyi and published by Springer. This book was released on 2013-12-30 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains three interrelated, beautiful, and useful topics of quantum scattering theory: inverse scattering theory, algebraic scattering theory and supersymmetrical quantum mechanics. The contributions cover such issues as coupled-channel inversions at fixed energy, inversion of pion-nucleon scattering cross-sections into potentials, inversions in neutron and x-ray reflection, 3-dimensional fixed-energy inversion, inversion of electron scattering data affected by dipole polarization, nucleon-nucleon potentials by inversion versus meson-exchange theory, potential reversal and reflectionless impurities in periodic structures, quantum design in spectral, scattering, and decay control, solution hierarchy of Toda lattices, etc.
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 293 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.
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 Theory and Application of Quantum Molecular Dynamics written by John Z. H. Zhang and published by World Scientific. This book was released on 1999 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an updated and detailed presentation of modern quantum-mechanical treatments and practical computational methods for dynamical processes of small molecular systems. The main emphasis is on the recent development of successful theories and computational methods for the reactive scattering process. Specific applications are given in detail for a number of benchmark chemical reaction systems in the gas phase and gas surface. Differing from traditional physics books focusing on abstract collision theory for elastic collisions, the book has been written in a fashion in which the development of general reactive or rearrangement scattering theory is accompanied by practical applications for realistic reaction systems.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1974 with total page 1286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The High Energy Phase Shift in Potential Scattering written by T. Dolinszky and published by . This book was released on 1975 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Theory Of Tunneling 2nd Edition written by Mohsen Razavy and published by World Scientific. This book was released on 2013-12-17 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this revised and expanded edition, in addition to a comprehensible introduction to the theoretical foundations of quantum tunneling based on different methods of formulating and solving tunneling problems, different semiclassical approximations for multidimensional systems are presented. Particular attention is given to the tunneling of composite systems, with examples taken from molecular tunneling and also from nuclear reactions. The interesting and puzzling features of tunneling times are given extensive coverage, and the possibility of measurement of these times with quantum clocks are critically examined.In addition, by considering the analogy between evanescent waves in waveguides and in quantum tunneling, the times related to electromagnetic wave propagation have been used to explain certain aspects of quantum tunneling times. These topics are treated in both non-relativistic as well as relativistic regimes. Finally, a large number of examples of tunneling in atomic, molecular, condensed matter and nuclear physics are presented and solved.
Download or read book Theory of Reflection of Electromagnetic and Particle Waves written by John Lekner and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written for scientists and engineers whose work involves wave reflec tion or transmission. Most of the book is written in the language of electromagnetic theory, but, as the title suggests, many of the results can be applied to particle waves, specifically to those satisfying the Schr6dinger equation. The mathematical connection between electromagnetic s (or TE) waves and quantum particle waves is established in Chapter 1. The main results for s waves are translated into quantum mechanical language in the Appendix. There is also a close analogy between acoustic waves and electromagnetic p (or TM) waves, as shown in Section 1-4. Thus the book, though primarily intended for those working in optics, microwaves and radio, will be of use to physicists, chemists and electrical engineers studying reflection and transmission of particles at potential barriers. The tech niques developed here can also be used by those working in acoustics, ocean ography and seismology. Chapter 1 is recommended for all readers: it introduces reflection phenomena, defines the notation, and previews (in Section 1-6) the contents of the rest of the book. This preview will not be duplicated here. We note only that applied topics do appear: two examples are the important phenomenon of attenuated total reflection in Chapter 8, and the reflectivity of multilayer dielectric mirrors in Chapter 12. The subject matter is restricted to linear classical electrodynamics in non-magnetic media, and the corresponding particle analogues.
