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Author : John von Neumann
Publisher : Princeton University Press
Page : 462 pages
File Size : 43,6 Mb
Release : 1955
Category : Mathematics
ISBN : 0691028931
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
Page : 256 pages
File Size : 50,9 Mb
Release : 2013-02-21
Category : Mathematics
ISBN : 9780486167657
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 : Aleksandr I︠A︡kovlevich Khinchin
Publisher : Unknown
Page : 252 pages
File Size : 43,7 Mb
Release : 1960
Category : Science
ISBN : STANFORD:36105020097338
Author : Aleksandr Iakovlevich Khinchin
Publisher : Unknown
Page : 128 pages
File Size : 48,9 Mb
Release : 1949-06-01
Category : Electronic
ISBN : 0486697576
Author : D.Y. Petrina
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401101851
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.
Author : A.R. Marlow
Publisher : Elsevier
Page : 382 pages
File Size : 46,7 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323141185
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 : Aleksandr I?Akovlevich Khinchin
Publisher : Courier Corporation
Page : 212 pages
File Size : 44,6 Mb
Release : 1949-01-01
Category : Mathematics
ISBN : 0486601471
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 : Alexander S. Holevo
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 45,9 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540449980
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 : Marco Tomamichel
Publisher : Springer
Page : 138 pages
File Size : 53,7 Mb
Release : 2015-10-14
Category : Science
ISBN : 9783319218915
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 : D.Ya. Petrina,V.I. Gerasimenko,P V Malyshev
Publisher : CRC Press
Page : 352 pages
File Size : 51,7 Mb
Release : 2002-04-11
Category : Science
ISBN : 0415273544
This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov equations for the sequences of correlation functions in the thermodynamic limit. This is the first detailed investigation of the thermodynamic limit for non-equilibrium systems and of the states of infinite systems in the cases of both canonical and grand canonical ensembles, for which the thermodynamic equivalence is proved. A comprehensive survey of results is also included; it concerns the properties of correlation functions for infinite systems and the corresponding equations. For this new edition, the authors have made changes to reflect the development of theory in the last ten years. They have also simplified certain sections, presenting them more systematically, and greatly increased the number of references. The book is aimed at theoretical physicists and mathematicians and will also be of use to students and postgraduate students in the field.
Author : K.R. Parthasarathy
Publisher : Springer
Page : 175 pages
File Size : 52,9 Mb
Release : 2005-10-15
Category : Mathematics
ISBN : 9789386279286
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 : Dr. Gérard G. Emch
Publisher : Courier Corporation
Page : 352 pages
File Size : 48,8 Mb
Release : 2014-08-04
Category : Science
ISBN : 9780486151717
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 : Alexander S. Holevo
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 50,6 Mb
Release : 2011-05-05
Category : Mathematics
ISBN : 9788876423789
This book is devoted to aspects of the foundations of quantum mechanics in which probabilistic and statistical concepts play an essential role. The main part of the book concerns the quantitative statistical theory of quantum measurement, based on the notion of positive operator-valued measures. During the past years there has been substantial progress in this direction, stimulated to a great extent by new applications such as Quantum Optics, Quantum Communication and high-precision experiments. The questions of statistical interpretation, quantum symmetries, theory of canonical commutation relations and Gaussian states, uncertainty relations as well as new fundamental bounds concerning the accuracy of quantum measurements, are discussed in this book in an accessible yet rigorous way. Compared to the first edition, there is a new Supplement devoted to the hidden variable issue. Comments and the bibliography have also been extended and updated.
Author : Valter Moretti
Publisher : Springer
Page : 950 pages
File Size : 47,6 Mb
Release : 2018-01-30
Category : Mathematics
ISBN : 9783319707068
This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."
Author : STEPHEN J. GUSTAFSON
Publisher : Unknown
Page : 128 pages
File Size : 42,5 Mb
Release : 2020
Category : Mathematics
ISBN : 9783030595623
The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.