Download or read book Formulations of Classical and Quantum Dynamical Theory written by and published by Elsevier. This book was released on 1969-02-12 with total page 322 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 Formulations of Classical and Quantum Dynamical Theory written by Gerald Rosen and published by . This book was released on 1969 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Formulations of Classical and Quantum Dynamical Theory written by Gerald Rosen and published by . This book was released on 1969 with total page 151 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.
Download or read book Geometric Formulation of Classical and Quantum Mechanics written by G. Giachetta and published by World Scientific. This book was released on 2011 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.
Download or read book Classical and Quantum Dynamics written by Walter Dittrich and published by Springer. This book was released on 2015-10-08 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name a few. Well-chosen and detailed examples illustrate the perturbation theory, canonical transformations, the action principle and demonstrate the usage of path integrals. This new edition has been revised and enlarged with chapters on quantum electrodynamics, high energy physics, Green’s functions and strong interaction. "This book is a brilliant exposition of dynamical systems covering the essential aspects and written in an elegant manner. The book is written in modern language of mathematics and will ideally cater to the requirements of graduate and first year Ph.D. students...a wonderful introduction to any student who wants to do research in any branch of theoretical Physics." (Indian Journal of Physics)
Download or read book Dynamics of Classical and Quantum Fields written by Girish S. Setlur and published by Taylor & Francis. This book was released on 2013-12-05 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamics of Classical and Quantum Fields: An Introduction focuses on dynamical fields in non-relativistic physics. Written by a physicist for physicists, the book is designed to help readers develop analytical skills related to classical and quantum fields at the non-relativistic level, and think about the concepts and theory through numerous probl
Download or read book Group Theory and Its Applications written by Ernest M. Loebl and published by Academic Press. This book was released on 2014-05-10 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group Theory and its Applications, Volume III covers the two broad areas of applications of group theory, namely, all atomic and molecular phenomena, as well as all aspects of nuclear structure and elementary particle theory. This volume contains five chapters and begins with an introduction to Wedderburn’s theory to establish the structure of semisimple algebras, algebras of quantum mechanical interest, and group algebras. The succeeding chapter deals with Dynkin’s theory for the embedding of semisimple complex Lie algebras in semisimple complex Lie algebras. These topics are followed by a review of the Frobenius algebra theory, its centrum, its irreducible, invariant subalgebras, and its matric basis. The discussion then shifts to the concepts and application of the Heisenberg-Weyl ring to quantum mechanics. Other chapters explore some well-known results about canonical transformations and their unitary representations; the Bargmann Hilbert spaces; the concept of complex phase space; and the concept of quantization as an eigenvalue problem. The final chapter looks into a theoretical approach to elementary particle interactions based on two-variable expansions of reaction amplitudes. This chapter also demonstrates the use of invariance properties of space-time and momentum space to write down and exploit expansions provided by the representation theory of the Lorentz group for relativistic particles, or the Galilei group for nonrelativistic ones. This book will prove useful to mathematicians, engineers, physicists, and advance students.
Download or read book The Historical Development of Quantum Theory written by Jagdish Mehra and published by Springer Science & Business Media. This book was released on 2000-12-28 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Theory, together with the principles of special and general relativity, constitute a scientific revolution that has profoundly influenced the way in which we think about the universe and the fundamental forces that govern it. The Historical Development of Quantum Theory is a definitive historical study of that scientific work and the human struggles that accompanied it from the beginning. Drawing upon such materials as the resources of the Archives for the History of Quantum Physics, the Niels Bohr Archives, and the archives and scientific correspondence of the principal quantum physicists, as well as Jagdish Mehra's personal discussions over many years with most of the architects of quantum theory, the authors have written a rigorous scientific history of quantum theory in a deeply human context. This multivolume work presents a rich account of an intellectual triumph: a unique analysis of the creative scientific process. The Historical Development of Quantum Theory is science, history, and biography, all wrapped in the story of a great human enterprise. Its lessons will be an aid to those working in the sciences and humanities alike.
Download or read book Classical Dynamics and Its Quantum Analogues written by David Park and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: The short Heroic Age of physics that started in 1925 was one of the rare occasions when a deep consideration of the question: What does physics really say? was necessary in carrying out numerical calculations. In many parts of microphysics the calculations have now become relatively straightforward if not easy, but most physicists seem to agree that some questions of principle remain to be resolved, even if they do not think it is very important to do so. This situation has affected the way people think and write about quantum mechanics, a gingerly approach to fundamentals and a tendency to emphasize what fifty years ago was new in the new theory at the expense of continuity with what came before it. Nowadays those who look into the subject are more likely to be struck by unexpected similarities between quantum and classical mechanics than by dramatic contrasts they had been led to expect. It is often said that the hardest part of understanding quantum mechanics is to understand that there is nothing to understand; all the same, to think quantum mechanically it helps to have firm mental connections with classical physics and to know exactly what these connections do and do not imply. This book originated more than a decade ago as informal lecture notes [OP, prepared for use in a course taught from time to time to advanced undergraduates at Williams College.
Download or read book Classical Mechanics Quantum Mechanics Field Theory written by Amnon Katz and published by . This book was released on 1965 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description: This book explores a fundamental tension in Aristotle's metaphysics: how can an entity such as a living organisma composite generated through the imposition of form on preexisting matterhave the conceptual unity that Aristotle demands of primary substances? Mary Louise Gill bases her treatment of the problem of unity, and of Aristotle's solution, on a fresh interpretation of the relation between matter and form. Challenging the traditional understanding of Aristotelian matter, she argues that material substances are subverted by matter and maintained by form that controls the matter to serve a positive end. The unity of material substances thus involves a dynamic relation between resistant materials and directive ends. Aristotle on Substance offers both a general account of matter, form, and substantial unity and a specific assessment of particular Aristotelian arguments. At every point, Gill engages Aristotle on his own philosophical ground through the detailed analysis of central, and often controversial, texts from the Metaphysics, Physics, On Generation and Corruption, De Anima, De Caelo, and the biological works. The result is a coherent, firmly grounded rethinking of Aristotle's central metaphysical concepts and of his struggle toward a fully consistent theory of material substances.
Download or read book Contemporary Research in the Foundations and Philosophy of Quantum Theory written by C.A. Hooker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: To mathematicians, mathematics is a happy game, to scientists a mere tool and to philosophers a Platonic mystery - or so the caricature runs. The caricature reflects the alleged 'cultural gap' between the disciplines a gap for which there too often has been, sadly, sound historical evidence. In many minds the lack of communication between philosophy and the exact disciplines is especially prominent. Yet in the past there was no separation - exact knowledge, covering both scientists and mathemati cians, was known as natural philosophy and the business of providing a critical view of the nature of reality and an accurate mathematical de scription of it constituted a single task from the glorious tradition begun by the early Greek philosophers even up until Newton's day (but I am thinking of Descartes and Leibniz I). The lack of communication between these professional groups has been particularly unfortunate, for the past half century has seen the most ex citing developments in mathematical physics since Newton. These devel opments hinged on the introduction of vast new reaches of mathematics into physics (non-Euclidean geometries, covariant formulations, non commutative algebras, functional analysis and so on) and conversely have challenged mathematicians to develop the appropriate mathematical fields. Equally, these developments have posed profound philosophical problems to do with the rejection of traditional conceptions concerning the nature of physical reality and physical theorising.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1974 with total page 1174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamics Information and Complexity in Quantum Systems written by Fabio Benatti and published by Springer Science & Business Media. This book was released on 2009-04-17 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a self-contained overview of the entropic approach to quantum dynamical systems. In it, complexity in quantum dynamics is addressed by comparison with the classical ergodic, information, and algorithmic complexity theories.
Download or read book Advances In Dynamical Systems And Quantum Physics Proceedings Of The Conference written by Sergio Albeverio and published by World Scientific. This book was released on 1995-02-23 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions from the meeting held in honour of G.F. Dell'Antonio for his sixtieth birthday. The topics covered include the theory of classical and quantum dynamical systems and related mathematical disciplines such as functional and stochastic analysis, operator algebras etc. The contributions by leading specialists survey recent developments in Hamiltonian dynamics, non-commutative integration, supersymmetric theories, spin glass theory and other subjects in mathematical physics.
Download or read book The Quantum Classical Theory written by Gert D. Billing and published by Oxford University Press. This book was released on 2003-01-23 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over a period of fifty years, the quantum-classical or semi-classical theories have been among the most popular for calculations of rates and cross sections for many dynamical processes: energy transfer, chemical reactions, photodissociation, surface dynamics, reactions in clusters and solutions, etc. These processes are important in the simulation of kinetics of processes in plasma chemistry, chemical reactors, chemical or gas lasers, atmospheric and interstellar chemistry, as well as various industrial processes. This book gives an overview of quantum-classical methods that are currently used for a theoretical description of these molecular processes. It gives the theoretical background for the derivation of the theories from first principles. Enough details are provided to allow numerical implementation of the methods. The book gives the necessary background for understanding the approximations behind the methods and the working schemes for treating energy transfer processes from diatomic to polyatomic molecules, reactions at surfaces, non-adiabatic processes, and chemical reactions.
Download or read book Paradigms and Paradoxes written by Robert G. Colodny and published by University of Pittsburgh Pre. This book was released on 2010-11-23 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: The revolution involving the foundations of the physical sciences heralded by relativity and quantum theories has been stimulating philosophers for many years. Both of these comprehensive sets of concepts have involved profound challenges to traditional theories of epistemology, ontology, and language. This volume gathers six experts in physics, logic and philosophy to discuss developments in space exploration and nuclear science and their impact on the philosophy of science.
Download or read book Classical And Quantum Dissipative Systems Second Edition written by Razavy Mohsen and published by World Scientific. This book was released on 2017-02-27 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dissipative forces play an important role in problems of classical as well as quantum mechanics. Since these forces are not among the basic forces of nature, it is essential to consider whether they should be treated as phenomenological interactions used in the equations of motion, or they should be derived from other conservative forces. In this book we discuss both approaches in detail starting with the Stoke's law of motion in a viscous fluid and ending with a rather detailed review of the recent attempts to understand the nature of the drag forces originating from the motion of a plane or a sphere in vacuum caused by the variations in the zero-point energy. In the classical formulation, mathematical techniques for construction of Lagrangian and Hamiltonian for the variational formulation of non-conservative systems are discussed at length. Various physical systems of interest including the problem of radiating electron, theory of natural line width, spin-boson problem, scattering and trapping of heavy ions and optical potential models of nuclear reactions are considered and solved.
