Download or read book Chaos in Classical and Quantum Mechanics written by Martin C. Gutzwiller and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.
Download or read book Mathematics of Classical and Quantum Physics written by Frederick W. Byron and published by Courier Corporation. This book was released on 2012-04-26 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.
Download or read book From Classical to Quantum Mechanics written by Giampiero Esposito and published by Cambridge University Press. This book was released on 2004-03-11 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the Cauchy problem for the wave equation, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to aid the reader's understanding.
Download or read book Mathematical Topics Between Classical and Quantum Mechanics written by Nicholas P. Landsman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph draws on two traditions: the algebraic formulation of quantum mechanics as well as quantum field theory, and the geometric theory of classical mechanics. These are combined in a unified treatment of the theory of Poisson algebras of observables and pure state spaces with a transition probability, which leads on to a discussion of the theory of quantization and the classical limit from this perspective. A prototype of quantization comes from the analogy between the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel between reduction of symplectic manifolds in classical mechanics and induced representations of groups and C*- algebras in quantum mechanics plays an equally important role. Examples from physics include constrained quantization, curved spaces, magnetic monopoles, gauge theories, massless particles, and $theta$- vacua. Accessible to mathematicians with some prior knowledge of classical and quantum mechanics, and to mathematical physicists and theoretical physicists with some background in functional analysis.
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 A Brief Introduction to Classical Statistical and Quantum Mechanics written by Oliver Bühler and published by American Mathematical Soc.. This book was released on 2006-10-12 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a rapid overview of the basic methods and concepts in mechanics for beginning Ph.D. students and advanced undergraduates in applied mathematics or related fields. It is based on a graduate course given in 2006-07 at the Courant Institute of Mathematical Sciences. Among other topics, the book introduces Newton's law, action principles, Hamilton-Jacobi theory, geometric wave theory, analytical and numerical statistical mechanics, discrete and continuous quantum mechanics, and quantum path-integral methods. The focus is on fundamental mathematical methods that provide connections between seemingly unrelated subjects. An example is Hamilton-Jacobi theory, which appears in the calculus of variations, in Fermat's principle of classical mechanics, and in the geometric theory of dispersive wavetrains. The material is developed in a sequence of simple examples and the book can be used in a one-semester class on classical, statistical, and quantum mechanics. Some familiarity with differential equations is required but otherwise the book is self-contained. In particular, no previous knowledge of physics is assumed. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Download or read book Advanced Quantum Mechanics written by Reinhold Blumel and published by Jones & Bartlett Publishers. This book was released on 2010-04-28 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a coherent introduction to Gutzwiller’s trace formula accessible to well-prepared science, mathematics, and engineering students who have taken introductory courses in linear algebra, classical, and quantum mechanics. In addition to providing an enrichment of the undergraduate curriculum, this book may serve as the primary text for graduate courses on semiclassical methods. Since periodic-orbit expansions may be used to solve all types of wave systems that typically occur in mathematics, phyics, and engineering, this book is attractice for professional scientists and engineers as well. Following a thorough review of elementary concepts in classical and quantum mechanics the reader is introduced to the idea of classical periodic orbits, the foundation of Gutzwiller’s approach to quantum spectra. The trace formula itself is derived following an introduction to Feynman’s path integrals. Numerous applications, including the exact solutions of “unsolvable” one-dimensional quantum problems, illustrate the power of Gutzwiller’s method. Worked examples throughout the text illustrate the material and provide immediate “hands-on” demonstrations of tools and concepts just learned. Problems at the end of each section invite the reader to consolidate the acquired knowledge.
Download or read book Geometric Phases in Classical and Quantum Mechanics written by Dariusz Chruscinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.
Download or read book Problems in Classical and Quantum Mechanics written by J. Daniel Kelley and published by Springer. This book was released on 2016-11-30 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of problems that are intended to aid students in graduate and undergraduate courses in Classical and Quantum Physics. It is also intended to be a study aid for students that are preparing for the PhD qualifying exam. Many of the included problems are of a type that could be on a qualifying exam. Others are meant to elucidate important concepts. Unlike other compilations of problems, the detailed solutions are often accompanied by discussions that reach beyond the specific problem.The solution of the problem is only the beginning of the learning process--it is by manipulation of the solution and changing of the parameters that a great deal of insight can be gleaned. The authors refer to this technique as "massaging the problem," and it is an approach that the authors feel increases the pedagogical value of any problem.
Download or read book Classical Systems in Quantum Mechanics written by Pavel Bóna and published by Springer Nature. This book was released on 2020-06-23 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems – i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of “quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".
Download or read book Classical and Quantum Information written by Dan C. Marinescu and published by Academic Press. This book was released on 2011-01-07 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new discipline, Quantum Information Science, has emerged in the last two decades of the twentieth century at the intersection of Physics, Mathematics, and Computer Science. Quantum Information Processing is an application of Quantum Information Science which covers the transformation, storage, and transmission of quantum information; it represents a revolutionary approach to information processing. Classical and Quantum Information covers topics in quantum computing, quantum information theory, and quantum error correction, three important areas of quantum information processing. Quantum information theory and quantum error correction build on the scope, concepts, methodology, and techniques developed in the context of their close relatives, classical information theory and classical error correcting codes. - Presents recent results in quantum computing, quantum information theory, and quantum error correcting codes - Covers both classical and quantum information theory and error correcting codes - The last chapter of the book covers physical implementation of quantum information processing devices - Covers the mathematical formalism and the concepts in Quantum Mechanics critical for understanding the properties and the transformations of quantum information
Download or read book Introductory Quantum Mechanics written by Paul R. Berman and published by Springer. This book was released on 2017-12-26 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a basic introduction to quantum mechanics. Depending on the choice of topics, it can be used for a one-semester or two-semester course. An attempt has been made to anticipate the conceptual problems students encounter when they first study quantum mechanics. Wherever possible, examples are given to illustrate the underlying physics associated with the mathematical equations of quantum mechanics. To this end, connections are made with corresponding phenomena in classical mechanics and electromagnetism. The problems at the end of each chapter are intended to help students master the course material and to explore more advanced topics. Many calculations exploit the extraordinary capabilities of computer programs such as Mathematica, MatLab, and Maple. Students are urged to use these programs, just as they had been urged to use calculators in the past. The treatment of various topics is rather complete, in that most steps in derivations are included. Several of the chapters go beyond what is traditionally covered in an introductory course. The goal of the presentation is to provide the students with a solid background in quantum mechanics.
Download or read book Quantum Mechanics written by Leonard Susskind and published by Basic Books (AZ). This book was released on 2014-02-25 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the bestselling author of The Theoretical Minimum, a DIY introduction to the math and science of quantum physics First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics. In this follow-up to The Theoretical Minimum, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions. Unlike other popularizations that shy away from quantum mechanics’ weirdness, Quantum Mechanics embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area. Like The Theoretical Minimum, this volume runs parallel to Susskind’s eponymous Stanford University-hosted continuing education course. An approachable yet rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.
Download or read book Quantum Classical Correspondence written by A. O. Bolivar and published by Springer Science & Business Media. This book was released on 2004-01-22 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. It elucidates the problem of quantum-classical correspondence by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Graduate students and physical scientists will find this an accessible entrée to an intriguing and thorny issue at the core of modern physics.
Download or read book Classical and Quantum Mechanics with Lie Algebras written by Yair Shapira and published by . This book was released on 2021 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Mechanics and Quantum Field Theory written by Jonathan Dimock and published by Cambridge University Press. This book was released on 2011-02-03 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explaining the concepts of quantum mechanics and quantum field theory in a precise mathematical language, this textbook is an ideal introduction for graduate students in mathematics, helping to prepare them for further studies in quantum physics. The textbook covers topics that are central to quantum physics: non-relativistic quantum mechanics, quantum statistical mechanics, relativistic quantum mechanics and quantum field theory. There is also background material on analysis, classical mechanics, relativity and probability. Each topic is explored through a statement of basic principles followed by simple examples. Around 100 problems throughout the textbook help readers develop their understanding.
Download or read book Foundations of Classical and Quantum Statistical Mechanics written by R. Jancel and published by Elsevier. This book was released on 2013-10-22 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Classical and Quantum Statistical Mechanics details the theoretical foundation the supports the concepts in classical and quantum statistical mechanics. The title discusses the various problems set by the theoretical justification of statistical mechanics methods. The text first covers the the ergodic theory in classical statistical mechanics, and then proceeds to tackling quantum mechanical ensembles. Next, the selection discusses the the ergodic theorem in quantum statistical mechanics and probability quantum ergodic theorems. The selection also details H-theorems and kinetic equations in classical and quantum statistical mechanics. The book will be of great interest to students, researchers, and practitioners of physics, chemistry, and engineering.
