Emergence Of The Quantum From The Classical Mathematical Aspects Of Quantum Processes

Author : De Gosson Maurice A
Publisher : World Scientific
ISBN 13 : 1786344165
Total Pages : 308 pages
Book Rating : 4.68/5 ( download)

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Download or read book Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes written by De Gosson Maurice A and published by World Scientific. This book was released on 2017-11-10 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical. Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field. Contents: Hamiltonian MechanicsHamilton–Jacobi TheoryMatter Waves, Schrödinger's Equation, and Bohm's Theory The MetatronUncertainties and Quantum BlobsQuantum States and the Density MatrixVarying Planck's ConstantAppendices: The Symplectic GroupThe Metaplectic RepresentationBorn–Jordan QuantizationTwisted Product and Convolution Readership: Undergraduate and graduate students of mathematics and physics, interested in analysis and differential equations, probability and statistics, geometry and topology and mathematical physics. Keywords: Classical Mechanics;Hamiltonian Mechanics;Quantum Mechanics;Planck's Constant;Mathematical Physics;Algebraic GeometryReview:0

Author : Maurice A. De Gosson
Publisher :
ISBN 13 : 9781786344151
Total Pages : 306 pages
Book Rating : 4.57/5 ( download)

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Download or read book Emergence of the Quantum from the Classical written by Maurice A. De Gosson and published by . This book was released on 2017 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Maurice A. de Gosson
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110722909
Total Pages : 247 pages
Book Rating : 4.01/5 ( download)

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Download or read book Quantum Harmonic Analysis written by Maurice A. de Gosson and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-07-05 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.

Author : Ruth E Kastner
Publisher : World Scientific
ISBN 13 : 1786341425
Total Pages : 500 pages
Book Rating : 4.26/5 ( download)

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Download or read book Quantum Structural Studies written by Ruth E Kastner and published by World Scientific. This book was released on 2016-11-10 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The structural aspects of composite quantum systems in the foundation, interpretation and application of quantum theory is an increasingly prominent topic of physics research. As an emerging field, it seeks to understand the origins of the classical world of experience from the quantum level. Quantum Structural Studies presents conceptual fundamentals and mathematical methods for investigating the structuring of quantum systems into subsystems. Split into four sections, the topics covered include the historical and philosophical aspects of quantum structures, specific interpretive approaches and ontologies, and alternative methodological approaches to quantum mechanics. Questions addressed are: Can the classically relevant degrees of freedom (such as the center of mass) be considered physically realistic, and if so, in what sense?In what sense might various emergent structures be relevant for the transition from the quantum description to the classical?Do suggested new approaches describe phenomenology and proposals for new experiments? Specialists, graduate students and researchers seeking an introduction to the field of emergent structures and new directions for research and experimentation can use this book to find up-to-date representative texts and reviews.

Author : Daniel F. Styer
Publisher : Cambridge University Press
ISBN 13 : 1316101878
Total Pages : 248 pages
Book Rating : 4.72/5 ( download)

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Download or read book The Strange World of Quantum Mechanics written by Daniel F. Styer and published by Cambridge University Press. This book was released on 2000-02-24 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an exceptionally accessible, accurate, and non-technical introduction to quantum mechanics. After briefly summarizing the differences between classical and quantum behaviour, this engaging account considers the Stern-Gerlach experiment and its implications, treats the concepts of probability, and then discusses the Einstein-Podolsky-Rosen paradox and Bell's theorem. Quantal interference and the concept of amplitudes are introduced and the link revealed between probabilities and the interference of amplitudes. Quantal amplitude is employed to describe interference effects. Final chapters explore exciting new developments in quantum computation and cryptography, discover the unexpected behaviour of a quantal bouncing-ball, and tackle the challenge of describing a particle with no position. Thought-provoking problems and suggestions for further reading are included. Suitable for use as a course text, The Strange World of Quantum Mechanics enables students to develop a genuine understanding of the domain of the very small. It will also appeal to general readers seeking intellectual adventure.

Author : Herbert S. Green
Publisher : Springer Science & Business Media
ISBN 13 : 364257162X
Total Pages : 248 pages
Book Rating : 4.26/5 ( download)

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Download or read book Information Theory and Quantum Physics written by Herbert S. Green and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this highly readable book, H.S. Green, a former student of Max Born and well known as an author in physics and in the philosophy of science, presents a timely analysis of theoretical physics and related fundamental problems.

Author : Ignazio Licata
Publisher : World Scientific
ISBN 13 : 9812779949
Total Pages : 432 pages
Book Rating : 4.46/5 ( download)

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Download or read book Physics of Emergence and Organization written by Ignazio Licata and published by World Scientific. This book was released on 2008 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a state-of-the-art review on the Physics of Emergence. The challenge of complexity is to focus on the description levels of the observer in context-dependent situations. Emergence is not only an heuristic approach to complexity, but it also urges us to face a much deeper question ? what do we think is fundamental in the physical world?This volume provides significant and pioneering contributions based on rigorous physical and mathematical approaches ? with particular reference to the syntax of Quantum Physics and Quantum Field Theory ? dealing with the bridge-laws and their limitations between Physics and Biology, without failing to discuss the involved epistemological features.Physics of Emergence and Organization is an interdisciplinary source of reference for students and experts whose interests cross over to complexity issues.

Author : Robert Carroll
Publisher : World Scientific
ISBN 13 : 9814291803
Total Pages : 288 pages
Book Rating : 4.04/5 ( download)

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Download or read book On the Emergence Theme of Physics written by Robert Carroll and published by World Scientific. This book was released on 2010 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys mathematical relations between classical and quantum mechanics, gravity, time and thermodynamics from various points of view and many sources (with appropriate attribution). The emergence theme is developed with an emphasis on the meaning via mathematics. A background theme of Bohemian mechanics and connections to the quantum equivalence principle of Matone et al. is also developed in great detail. Some original work relating the quantum potential and Ricci flow is also included.

Author : Frederick W. Byron
Publisher : Courier Corporation
ISBN 13 : 0486135063
Total Pages : 674 pages
Book Rating : 4.69/5 ( download)

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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.

Author : Pavel Bóna
Publisher : Springer Nature
ISBN 13 : 3030450708
Total Pages : 243 pages
Book Rating : 4.00/5 ( download)

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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".