Mathematical Foundations Of Quantum Statistics

Mathematical Foundations of Quantum Statistics PDF
Author: A. Y. Khinchin
Publisher: Courier Corporation
ISBN: 0486167658
Size: 43.80 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 256
View: 2908

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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.

Mathematical Foundations Of Quantum Mechanics

Mathematical Foundations of Quantum Mechanics PDF
Author: John von Neumann
Publisher: Princeton University Press
ISBN: 9780691028934
Size: 37.53 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 445
View: 4178

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This text shows that insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. It presents the theory of Hermitean operators and Hilbert spaces, providing the framework for transformation theory, and using th

Mathematical Foundations Of Quantum Statistical Mechanics

Mathematical Foundations of Quantum Statistical Mechanics PDF
Author: D.Y. Petrina
Publisher: Springer Science & Business Media
ISBN: 940110185X
Size: 43.39 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 445
View: 296

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This monograph is devoted to quantum statistical mechanics. It can be regarded as a continuation of the book "Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems" (Gordon & Breach SP, 1989) written together with my colleagues V. I. Gerasimenko and P. V. Malyshev. Taken together, these books give a complete pre sentation of the statistical mechanics of continuous systems, both quantum and classical, from the common point of view. Both books have similar contents. They deal with the investigation of states of in finite systems, which are described by infinite sequences of statistical operators (reduced density matrices) or Green's functions in the quantum case and by infinite sequences of distribution functions in the classical case. The equations of state and their solutions are the main object of investigation in these books. For infinite systems, the solutions of the equations of state are constructed by using the thermodynamic limit procedure, accord ing to which we first find a solution for a system of finitely many particles and then let the number of particles and the volume of a region tend to infinity keeping the density of particles constant. However, the style of presentation in these books is quite different.

Mathematical Foundations Of Statistical Mechanics

Mathematical Foundations of Statistical Mechanics PDF
Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 9780486601472
Size: 40.80 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 179
View: 3571

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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.

Mathematical Foundations Of Quantum Theory

Mathematical Foundations of Quantum Theory PDF
Author: A.R. Marlow
Publisher: Elsevier
ISBN: 0323141188
Size: 64.83 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 382
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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.

Mathematical Foundation Of Quantum Mechanics

Mathematical Foundation of Quantum Mechanics PDF
Author: K.R. Parthasarathy
Publisher: Springer
ISBN: 9386279282
Size: 77.90 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 178
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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.

Mathematical Foundations Of Quantum Mechanics

Mathematical Foundations of Quantum Mechanics PDF
Author: George W. Mackey
Publisher: Courier Corporation
ISBN: 0486154475
Size: 59.96 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 160
View: 1300

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This graduate-level text introduces fundamentals of classical mechanics; surveys basics of quantum mechanics; and concludes with a look at group theory and quantum mechanics of the atom. 1963 edition.

Mathematical Foundations Of Statistical Mechanics

Mathematical Foundations of Statistical Mechanics PDF
Author: A. Ya. Khinchin
Publisher: Courier Corporation
ISBN: 0486138739
Size: 61.99 MB
Format: PDF
Category : Science
Languages : en
Pages : 179
View: 6198

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Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Reduction to the Problem of the Theory of Probability; and more.

Mathematical Foundations Of Quantum Mechanics

Mathematical Foundations of Quantum Mechanics PDF
Author: John von Neumann
Publisher: Princeton University Press
ISBN: 0691178577
Size: 74.43 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 328
View: 4546

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Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Foundations of Quantum Mechanics--a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Robert Beyer's 1955 English translation, which von Neumann reviewed and approved, is cited more frequently today than ever before. But its many treasures and insights were too often obscured by the limitations of the way the text and equations were set on the page. In this new edition of this classic work, mathematical physicist Nicholas Wheeler has completely reset the book in TeX, making the text and equations far easier to read. He has also corrected a handful of typographic errors, revised some sentences for clarity and readability, provided an index for the first time, and added prefatory remarks drawn from the writings of Léon Van Hove and Freeman Dyson. The result brings new life to an essential work in theoretical physics and mathematics.

Mathematical Foundations Of Classical Statistical Mechanics

Mathematical Foundations of Classical Statistical Mechanics PDF
Author: D. Ya. Petrina
Publisher: CRC Press
ISBN: 9782881246814
Size: 52.76 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 338
View: 785

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Introducing the functional method practiced in the USSR, this well- translated monograph considers the problem of investigating systems of infinite numbers of particles. It discusses the equilibrium and non- equilibrium states of infinite classical statistical systems, and investigates the thermodynamic limit for non-equilibrium systems and of the states of infinite systems, for which thermodynamic equivalence is proved. Book club price, $95. Annotation copyrighted by Book News, Inc., Portland, OR