Mathematical Foundations Of Quantum Statistics

Author : John von Neumann
Publisher : Princeton University Press
ISBN 13 : 9780691028934
Total Pages : 462 pages
Book Rating : 4.31/5 ( download)

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Download or read book Mathematical Foundations of Quantum Mechanics written by John von Neumann and published by Princeton University Press. This book was released on 1955 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revolutionary book that for the first time provided a rigorous mathematical framework for quantum mechanics. -- Google books

Author : A. Y. Khinchin
Publisher : Courier Corporation
ISBN 13 : 0486167658
Total Pages : 256 pages
Book Rating : 4.57/5 ( download)

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Download or read book Mathematical Foundations of Quantum Statistics written by A. Y. Khinchin and published by Courier Corporation. This book was released on 2013-02-21 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent, well-organized look at the basis of quantum statistics’ computational methods, the determination of the mean values of occupation numbers, the foundations of the statistics of photons and material particles, thermodynamics.

Author : A.R. Marlow
Publisher : Elsevier
ISBN 13 : 0323141188
Total Pages : 383 pages
Book Rating : 4.85/5 ( download)

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Download or read book Mathematical Foundations of Quantum Theory written by A.R. Marlow and published by Elsevier. This book was released on 2012-12-02 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fundamental quantum theory must deal, and then some unsolved problems in the quantum logic approach to the foundations of quantum mechanics are considered. Considerable chapters cover topics on manuals and logics for quantum mechanics. This book also examines the problems in quantum logic, and then presents examples of their interpretation and relevance to nonclassical logic and statistics. The accommodation of conventional Fermi-Dirac and Bose-Einstein statistics in quantum mechanics or quantum field theory is illustrated. The final chapters of the book present a system of axioms for nonrelativistic quantum mechanics, with particular emphasis on the role of density operators as states. Specific connections of this theory with other formulations of quantum theory are also considered. These chapters also deal with the determination of the state of an elementary quantum mechanical system by the associated position and momentum distribution. This book is of value to physicists, mathematicians, and researchers who are interested in quantum theory.

Author : Marco Tomamichel
Publisher : Springer
ISBN 13 : 3319218913
Total Pages : 138 pages
Book Rating : 4.15/5 ( download)

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Download or read book Quantum Information Processing with Finite Resources written by Marco Tomamichel and published by Springer. This book was released on 2015-10-14 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigations possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.

Author : Aleksandr Iakovlevich Khinchin
Publisher :
ISBN 13 : 9780486697574
Total Pages : pages
Book Rating : 4.76/5 ( download)

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Download or read book Mathematical Foundations of Quantum Statistics written by Aleksandr Iakovlevich Khinchin and published by . This book was released on 1949-06-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Aleksandr I?Akovlevich Khinchin
Publisher : Courier Corporation
ISBN 13 : 9780486601472
Total Pages : 212 pages
Book Rating : 4.71/5 ( download)

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Download or read book Mathematical Foundations of Statistical Mechanics written by Aleksandr I?Akovlevich Khinchin and published by Courier Corporation. This book was released on 1949-01-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.

Author : K.R. Parthasarathy
Publisher : Springer
ISBN 13 : 9386279282
Total Pages : 175 pages
Book Rating : 4.86/5 ( download)

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Download or read book Mathematical Foundation of Quantum Mechanics written by K.R. Parthasarathy and published by Springer. This book was released on 2005-10-15 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. The material in the first chapter is included in the author's book "An Introduction to Quantum Stochastic Calculus" published by Birkhauser Verlag in 1992 and the permission of the publishers to reprint it here is acknowledged. Apart from quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations in the second chapter. Based on a discussion of multipliers on locally compact groups in the third chapter all the well-known observables of classical quantum theory like linear momenta, orbital and spin angular momenta, kinetic and potential energies, gauge operators etc., are derived solely from Galilean covariance in the last chapter. A very short account of observables concerning a relativistic free particle is included. In conclusion, the spectral theory of Schrodinger operators of one and two electron atoms is discussed in some detail.

Author : Alexander S. Holevo
Publisher : Springer Science & Business Media
ISBN 13 : 3540449981
Total Pages : 166 pages
Book Rating : 4.80/5 ( download)

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Download or read book Statistical Structure of Quantum Theory written by Alexander S. Holevo and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.

Author : Dr. Gérard G. Emch
Publisher : Courier Corporation
ISBN 13 : 0486151719
Total Pages : 352 pages
Book Rating : 4.17/5 ( download)

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Download or read book Algebraic Methods in Statistical Mechanics and Quantum Field Theory written by Dr. Gérard G. Emch and published by Courier Corporation. This book was released on 2014-08-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This systematic algebraic approach offers a careful formulation of the problems' physical motivations as well as self-contained descriptions of the mathematical methods for arriving at solutions. 1972 edition.

Author : Paul Ehrenfest
Publisher : Courier Corporation
ISBN 13 : 0486163148
Total Pages : 128 pages
Book Rating : 4.47/5 ( download)

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Download or read book The Conceptual Foundations of the Statistical Approach in Mechanics written by Paul Ehrenfest and published by Courier Corporation. This book was released on 2014-11-12 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic 1912 article reformulated the foundations of the statistical approach in mechanics. Largely still valid, the treatment covers older formulation of statistico-mechanical investigations, modern formulation of kineto-statistics of the gas model, and more. 1959 edition.