Mathematical Foundations Of Quantum Mechanics

Mathematical Foundations of Quantum Mechanics PDF
Author: John von Neumann
Publisher: Princeton University Press
ISBN: 9780691028934
Size: 67.51 MB
Format: PDF, ePub, Docs
Category : Science
Languages : en
Pages : 445
View: 5209

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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 Statistical Mechanics

Mathematical Foundations of Statistical Mechanics PDF
Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 9780486601472
Size: 64.33 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 179
View: 5927

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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 Statistical Mechanics

Mathematical Foundations of Quantum Statistical Mechanics PDF
Author: D.Y. Petrina
Publisher: Springer Science & Business Media
ISBN: 940110185X
Size: 13.32 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 445
View: 4132

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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 Quantum Statistics

Mathematical Foundations of Quantum Statistics PDF
Author: A. Y. Khinchin
Publisher: Courier Corporation
ISBN: 0486167658
Size: 34.11 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 256
View: 7037

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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: George W. Mackey
Publisher: Courier Corporation
ISBN: 0486154475
Size: 67.60 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 160
View: 5342

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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 Foundation Of Quantum Mechanics

Mathematical Foundation of Quantum Mechanics PDF
Author: K.R. Parthasarathy
Publisher: Springer
ISBN: 9386279282
Size: 24.29 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 178
View: 3715

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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 Statistical Mechanics

Mathematical Foundations of Statistical Mechanics PDF
Author: A. Ya. Khinchin
Publisher: Courier Corporation
ISBN: 0486138739
Size: 55.46 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 179
View: 3995

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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 Classical Statistical Mechanics

Mathematical Foundations of Classical Statistical Mechanics PDF
Author: D.Ya. Petrina
Publisher: CRC Press
ISBN: 9780415273541
Size: 69.76 MB
Format: PDF, ePub
Category : Science
Languages : en
Pages : 352
View: 3951

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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.

Mathematical Foundations Of Quantum Mechanics

Mathematical Foundations of Quantum Mechanics PDF
Author: John von Neumann
Publisher: Princeton University Press
ISBN: 0691178569
Size: 12.16 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 328
View: 2520

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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 LĂ©on Van Hove and Freeman Dyson. The result brings new life to an essential work in theoretical physics and mathematics.

Philosophic Foundations Of Quantum Mechanics

Philosophic Foundations of Quantum Mechanics PDF
Author: Hans Reichenbach
Publisher: Courier Corporation
ISBN: 0486150100
Size: 34.93 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 208
View: 4691

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Noted philosopher offers a philosophical interpretation of quantum physics that reviews the basics of quantum mechanics and outlines their mathematical methods, blending philosophical ideas and mathematical formulations to develop a variety of concrete interpretations. 1944 edition.

The Theoretical Foundations Of Quantum Mechanics

The Theoretical Foundations of Quantum Mechanics PDF
Author: Belal E. Baaquie
Publisher: Springer Science & Business Media
ISBN: 146146224X
Size: 32.27 MB
Format: PDF, ePub, Docs
Category : Science
Languages : en
Pages : 268
View: 6508

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The Theoretical Foundations of Quantum Mechanics addresses fundamental issues that are not discussed in most books on quantum mechanics. This book focuses on analyzing the underlying principles of quantum mechanics and explaining the conceptual and theoretical underpinning of quantum mechanics. In particular, the concepts of quantum indeterminacy, quantum measurement and quantum superposition are analyzed to clarify the concepts that are implicit in the formulation of quantum mechanics. The Schrodinger equation is never solved in the book. Rather, the discussion on the fundamentals of quantum mechanics is treated in a rigorous manner based on the mathematics of quantum mechanics. The new concept of the interplay of empirical and trans-empirical constructs in quantum mechanics is introduced to clarify the foundations of quantum mechanics and to explain the counter-intuitive construction of nature in quantum mechanics. The Theoretical Foundations of Quantum Mechanics is aimed at the advanced undergraduate and assumes introductory knowledge of quantum mechanics. Its objective is to provide a solid foundation for the reader to reach a deeper understanding of the principles of quantum mechanics.

The Conceptual Foundations Of Quantum Mechanics

The Conceptual Foundations of Quantum Mechanics PDF
Author: Leonard Eisenbud
Publisher: American Mathematical Soc.
ISBN: 0821841793
Size: 37.36 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 148
View: 4411

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This book provides a clear and logical path to understanding what quantum mechanics is about. It will be accessible to undergraduates with minimal mathematical preparation: all that is required is an open mind, a little algebra, and a first course in undergraduate physics. Quantum mechanics is arguably the most successful physical theory. It makes predictions of incredible accuracy. It provides the structure underlying all of our electronic technology, and much of our mastery over materials. But compared with Newtonian mechanics, or even relativity, its teachings seem obscure--they have no counterpart in everyday experience, and they sometimes contradict our simplest notions of how the world works. A full understanding of the theory requires prior mastery of very advanced mathematics. This book aims at a different goal: to teach the reader, step by step, how the theory came to be and what, fundamentally, it is about. Most students learn physics by learning techniques and formulas. This is especially true in a field like quantum mechanics, whose content often contradicts our common sense, and where it's tempting to retreat into mathematical formalism. This book goes behind the formalism to explain in direct language the conceptual content and foundations of quantum mechanics: the experiments that forced physicists to construct such a strange theory, and the essential elements of its strangeness.