Mathematical Foundations of Quantum Mechanics by John Von Neumann

Title Mathematical Foundations of Quantum Mechanics
Author John Von Neumann
Publisher Princeton University Press
Release 1955
Category Mathematics
Total Pages 445
ISBN 0691028931
Language English, Spanish, and French

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Book Summary:

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 Mechanics by John von Neumann

Title Mathematical Foundations of Quantum Mechanics
Author John von Neumann
Publisher Princeton University Press
Release 2018-02-27
Category Science
Total Pages 328
ISBN 0691178577
Language English, Spanish, and French

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Book Summary:

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.

Spectral Theory and Quantum Mechanics by Valter Moretti

Title Spectral Theory and Quantum Mechanics
Author Valter Moretti
Publisher Springer
Release 2018-01-30
Category Mathematics
Total Pages 950
ISBN 331970706X
Language English, Spanish, and French

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Book Summary:

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."

Mathematical Foundations of Quantum Mechanics by John Von Neumann

Title Mathematical Foundations of Quantum Mechanics
Author John Von Neumann
Publisher
Release 1955
Category Science
Total Pages 445
ISBN 9780691080031
Language English, Spanish, and French

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Book Summary:

Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.

Mathematical Foundations of Quantum Mechanics by George W. Mackey

Title Mathematical Foundations of Quantum Mechanics
Author George W. Mackey
Publisher Courier Corporation
Release 2013-12-31
Category Mathematics
Total Pages 160
ISBN 0486154475
Language English, Spanish, and French

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Book Summary:

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.

John von Neumann and the Foundations of Quantum Physics by Miklós Rédei

Title John von Neumann and the Foundations of Quantum Physics
Author Miklós Rédei
Publisher Springer Science & Business Media
Release 2013-03-09
Category Science
Total Pages 373
ISBN 9401720126
Language English, Spanish, and French

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Book Summary:

John von Neumann (1903-1957) was undoubtedly one of the scientific geniuses of the 20th century. The main fields to which he contributed include various disciplines of pure and applied mathematics, mathematical and theoretical physics, logic, theoretical computer science, and computer architecture. Von Neumann was also actively involved in politics and science management and he had a major impact on US government decisions during, and especially after, the Second World War. There exist several popular books on his personality and various collections focusing on his achievements in mathematics, computer science, and economy. Strangely enough, to date no detailed appraisal of his seminal contributions to the mathematical foundations of quantum physics has appeared. Von Neumann's theory of measurement and his critique of hidden variables became the touchstone of most debates in the foundations of quantum mechanics. Today, his name also figures most prominently in the mathematically rigorous branches of contemporary quantum mechanics of large systems and quantum field theory. And finally - as one of his last lectures, published in this volume for the first time, shows - he considered the relation of quantum logic and quantum mechanical probability as his most important problem for the second half of the twentieth century. The present volume embraces both historical and systematic analyses of his methodology of mathematical physics, and of the various aspects of his work in the foundations of quantum physics, such as theory of measurement, quantum logic, and quantum mechanical entropy. The volume is rounded off by previously unpublished letters and lectures documenting von Neumann's thinking about quantum theory after his 1932 Mathematical Foundations of Quantum Mechanics. The general part of the Yearbook contains papers emerging from the Institute's annual lecture series and reviews of important publications of philosophy of science and its history.

Mathematical Foundation of Quantum Mechanics by K.R. Parthasarathy

Title Mathematical Foundation of Quantum Mechanics
Author K.R. Parthasarathy
Publisher Springer
Release 2005-10-15
Category Mathematics
Total Pages 178
ISBN 9386279282
Language English, Spanish, and French

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Book Summary:

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 Statistics by A. Y. Khinchin

Title Mathematical Foundations of Quantum Statistics
Author A. Y. Khinchin
Publisher Courier Corporation
Release 2013-02-21
Category Mathematics
Total Pages 256
ISBN 0486167658
Language English, Spanish, and French

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Book Summary:

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.