Quantum Classical Correspondence

Author : A. O. Bolivar
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 50,8 Mb
Release : 2013-04-09
Category : Science
ISBN : 9783662096499

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Quantum-Classical Correspondence by A. O. Bolivar Pdf

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.

Author : Bradley Clarke Hughes
Publisher : National Library of Canada = Bibliothèque nationale du Canada
Page : 208 pages
File Size : 44,7 Mb
Release : 1995
Category : Chaotic behavior in systems
ISBN : 0612066843

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Quantum-classical Correspondence in Two Simple Systems [microform] by Bradley Clarke Hughes Pdf

Author : Benjamin H. Feintzeig
Publisher : Cambridge University Press
Page : 141 pages
File Size : 47,9 Mb
Release : 2023-01-31
Category : Science
ISBN : 9781009049948

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The Classical–Quantum Correspondence by Benjamin H. Feintzeig Pdf

This Element provides an entry point for philosophical engagement with quantization and the classical limit. It introduces the mathematical tools of C*-algebras as they are used to compare classical and quantum physics. It then employs those tools to investigate philosophical issues surrounding theory change in physics. It discusses examples in which quantization bears on the topics of reduction, structural continuity, analogical reasoning, and theory construction. In doing so, it demonstrates that the precise mathematical tools of algebraic quantum theory can aid philosophers of science and philosophers of physics.

Author : Alisa Bokulich
Publisher : Cambridge University Press
Page : 0 pages
File Size : 43,9 Mb
Release : 2008-10-02
Category : Science
ISBN : 9780521857208

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Reexamining the Quantum-Classical Relation by Alisa Bokulich Pdf

The relation between quantum mechanics and classical mechanics, argued from historical, philosophical, and scientific perspectives.

Author : Gleb Arutyunov
Publisher : Springer
Page : 414 pages
File Size : 47,9 Mb
Release : 2019-07-23
Category : Science
ISBN : 9783030241988

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Elements of Classical and Quantum Integrable Systems by Gleb Arutyunov Pdf

Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

Author : Alexei Yu. Kitaev,Alexander Shen,Mikhail N. Vyalyi
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 45,9 Mb
Release : 2002
Category : Computers
ISBN : 9780821832295

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Classical and Quantum Computation by Alexei Yu. Kitaev,Alexander Shen,Mikhail N. Vyalyi Pdf

An introduction to a rapidly developing topic: the theory of quantum computing. Following the basics of classical theory of computation, the book provides an exposition of quantum computation theory. In concluding sections, related topics, including parallel quantum computation, are discussed.

Author : Olivier Darrigol
Publisher : University of California Press
Page : 412 pages
File Size : 42,8 Mb
Release : 2021-01-08
Category : Science
ISBN : 9780520328273

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From c-Numbers to q-Numbers by Olivier Darrigol Pdf

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1992.

Author : Sol Wieder
Publisher : Elsevier
Page : 416 pages
File Size : 53,5 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323141710

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The Foundations of Quantum Theory by Sol Wieder Pdf

The Foundations of Quantum Theory discusses the correspondence between the classical and quantum theories through the Poisson bracket-commutator analogy. The book is organized into three parts encompassing 12 chapters that cover topics on one-and many-particle systems and relativistic quantum mechanics and field theory. The first part of the book discusses the developments that formed the basis for the old quantum theory and the use of classical mechanics to develop the theory of quantum mechanics. This part includes considerable chapters on the formal theory of quantum mechanics and the wave mechanics in one- and three-dimension, with an emphasis on Coulomb problem or the hydrogen atom. The second part deals with the interacting particles and noninteracting indistinguishable particles and the material covered is fundamental to almost all branches of physics. The third part presents the pertinent equations used to illustrate the relativistic quantum mechanics and quantum field theory. This book is of value to undergraduate physics students and to students who have background in mechanics, electricity and magnetism, and modern physics.

Author : Niels Bohr
Publisher : Courier Corporation
Page : 132 pages
File Size : 48,7 Mb
Release : 2005-01-01
Category : Science
ISBN : 9780486442488

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On the Quantum Theory of Line-spectra by Niels Bohr Pdf

This classic work by the Nobel Laureate elaborates on the correspondence principle, discussing the theory's applications from a uniform point of view and considering the underlying assumptions in their relations to ordinary mechanics and electrodynamics. Bohr closely traces the analogy between quantum theory and ordinary theory of radiation. 1918-1922 editions.

Author : Martin Jähnert
Publisher : Springer
Page : 293 pages
File Size : 42,7 Mb
Release : 2019-06-20
Category : Science
ISBN : 9783030133009

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Practicing the Correspondence Principle in the Old Quantum Theory by Martin Jähnert Pdf

This book presents a history of the correspondence principle from a new perspective. The author provides a unique exploration of the relation between the practice of theory and conceptual development in physics. In the process, he argues for a new understanding of the history of the old quantum theory and the emergence of quantum mechanics. The analysis looks at how the correspondence principle was disseminated and how the principle was applied as a research tool during the 1920s. It provides new insights into the interaction between theoretical tools and scientific problems and shows that the use of this theoretical tool changed the tool itself in a process of transformation through implementation. This process, the author claims, was responsible for the conceptual development of the correspondence principle. This monograph connects to the vast literature in the history of science, which analyzed theoretical practices as based on tacit knowledge, skills, and calculation techniques. It contributes to the historical understanding of quantum physics and the emergence of quantum mechanics. Studying how physicists used a set of tools to solve problems, the author spells out the ‟skillful guessing” that went into the making of quantum theoretical arguments and argues that the integration and implementation of technical resources was a central driving force for the conceptual and theoretical transformation in the old quantum theory.

Author : Pedro de M. Rios,Eldar Straume
Publisher : Springer
Page : 204 pages
File Size : 42,5 Mb
Release : 2014-10-10
Category : Mathematics
ISBN : 9783319081984

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Symbol Correspondences for Spin Systems by Pedro de M. Rios,Eldar Straume Pdf

In mathematical physics, the correspondence between quantum and classical mechanics is a central topic, which this book explores in more detail in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems. A detailed presentation of quantum spin-j systems, with emphasis on the SO(3)-invariant decomposition of their operator algebras, is first followed by an introduction to the Poisson algebra of the classical spin system and then by a similarly detailed examination of its SO(3)-invariant decomposition. The book next proceeds with a detailed and systematic study of general quantum-classical symbol correspondences for spin-j systems and their induced twisted products of functions on the 2-sphere. This original systematic presentation culminates with the study of twisted products in the asymptotic limit of high spin numbers. In the context of spin systems it shows how classical mechanics may or may not emerge as an asymptotic limit of quantum mechanics. The book will be a valuable guide for researchers in this field and its self-contained approach also makes it a helpful resource for graduate students in mathematics and physics.

Author : Daniela Dragoman,Mircea Dragoman
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 51,9 Mb
Release : 2013-04-09
Category : Science
ISBN : 9783662096475

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Quantum-Classical Analogies by Daniela Dragoman,Mircea Dragoman Pdf

It is unanimously accepted that the quantum and the classical descriptions of the physical reality are very different, although any quantum process is "mysteriously" transformed through measurement into an observable classical event. Beyond the conceptual differences, quantum and classical physics have a lot in common. And, more important, there are classical and quantum phenomena that are similar although they occur in completely different contexts. For example, the Schrödinger equation has the same mathematical form as the Helmholtz equation, there is an uncertainty relation in optics very similar to that in quantum mechanics, and so on; the list of examples is very long. Quantum-classical analogies have been used in recent years to study many quantum laws or phenomena at the macroscopic scale, to design and simulate mesoscopic devices at the macroscopic scale, to implement quantum computer algorithms with classical means, etc. On the other hand, the new forms of light – localized light, frozen light – seem to have more in common with solid state physics than with classical optics. So these analogies are a valuable tool in the quest to understand quantum phenomena and in the search for new (quantum or classical) applications, especially in the area of quantum devices and computing.

Author : Daniel Greenberger,Klaus Hentschel,Friedel Weinert
Publisher : Springer Science & Business Media
Page : 901 pages
File Size : 44,9 Mb
Release : 2009-07-25
Category : Science
ISBN : 9783540706267

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Compendium of Quantum Physics by Daniel Greenberger,Klaus Hentschel,Friedel Weinert Pdf

With contributions by leading quantum physicists, philosophers and historians, this comprehensive A-to-Z of quantum physics provides a lucid understanding of key concepts of quantum theory and experiment. It covers technical and interpretational aspects alike, and includes both traditional and new concepts, making it an indispensable resource for concise, up-to-date information about the many facets of quantum physics.

Author : Martin C. Gutzwiller
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 50,7 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461209836

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Chaos in Classical and Quantum Mechanics by Martin C. Gutzwiller Pdf

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.

Author : Howard J. Carmichael
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 50,5 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783662038758

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Statistical Methods in Quantum Optics 1 by Howard J. Carmichael Pdf

This is the first of a two-volume presentation on current research problems in quantum optics, and will serve as a standard reference in the field for many years to come. The book provides an introduction to the methods of quantum statistical mechanics used in quantum optics and their application to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are discussed together with the more standard methods for deriving Fokker-Planck equations.