Mathematical Foundations Of Quantum Mechanics

Mathematical Foundations of Quantum Mechanics PDF
Author: John Von Neumann
Publisher: Princeton University Press
ISBN: 0691028931
Size: 37.32 MB
Format: PDF, Mobi
Category : Mathematics
Languages : un
Pages : 445
View: 1106

Get Book

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

Mathematical Foundations of Quantum Mechanics PDF
Author: John von Neumann
Publisher: Princeton University Press
ISBN: 0691178577
Size: 22.29 MB
Format: PDF, Mobi
Category : Science
Languages : un
Pages : 328
View: 6069

Get Book

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 Quantum Mechanics

Mathematical Foundations of Quantum Mechanics PDF
Author: George W. Mackey
Publisher: Courier Corporation
ISBN: 0486154475
Size: 52.43 MB
Format: PDF, Mobi
Category : Mathematics
Languages : un
Pages : 160
View: 706

Get Book

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 Quantum Theory

Mathematical Foundations of Quantum Theory PDF
Author: A.R. Marlow
Publisher: Elsevier
ISBN: 0323141188
Size: 51.75 MB
Format: PDF, Docs
Category : Science
Languages : un
Pages : 382
View: 1026

Get Book

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: 13.26 MB
Format: PDF, Mobi
Category : Mathematics
Languages : un
Pages : 178
View: 5677

Get Book

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

Mathematical Foundations of Quantum Statistics PDF
Author: A. Y. Khinchin
Publisher: Courier Corporation
ISBN: 0486167658
Size: 50.93 MB
Format: PDF, Docs
Category : Mathematics
Languages : un
Pages : 256
View: 1993

Get Book

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.

Die Grundlagen Der Quantenmechanik

Die Grundlagen der Quantenmechanik PDF
Author: Günther Ludwig
Publisher: Springer-Verlag
ISBN: 366211920X
Size: 77.34 MB
Format: PDF, Docs
Category : Mathematics
Languages : de
Pages : 460
View: 7574

Get Book

Mehrere Gründe bewogen mich, den Plan zu einem Buch über Quantenmechanik zu entwerfen, obwohl es in der Literatur schon manche Darstellung dieses Gebietes gibt. Einmal traf man bei den Lernenden immer wieder auf die Auf fassung, daß die Quantentheorie nur ein Provisorium der theoretischen Physik sei, aber zumindest noch einer genaueren Begründung bedürfe, da sowohl der mathematische Formalismus nicht exakt fundiert sei als auch die physikalische Interpretion sehr "nach Gefühl" in jedem Einzelfall durchgeführt würde. Nachdem das Buch von J. v. NEu MANN, Mathematische Grundlagen der Quantenmechanik, vergriffen war, konnte man kaum ein entsprechendes Werk empfehlen, das im physikalischen Zusammenhang die mathematischen Grundlagen klar legt. In dem vorliegenden Buche ist die eigentiiche Quantenmechamk (also ohne Feldtheorie) in der Weise dargestellt, daß man sie als em mathematisch wohlbegründetes und in sich genauso widerspruchs freies und abgeschlossenes System erkennt, wie die klassische Punkt mechanik. So wie die Kräfte, d. h. so wie die HAMILTON-Funktwn, in der klassischen Mechanik gegeben sein müssen, so m der Quanten mechanik der HAMILTON-Üperator. Die Herleitung eines Ansatzes für den HAMILTON-Operator eines Problems aus anderen Gebieten der Physik wird deshalb hier nicht näher begründet. Neben dem Wunsch, die Quantenmechamk als ein in sich geschlos senes Gebiet darzustellen, bestand ein zweiter Grund für die Abfassung des Buches in der inneren Harmonie zwischen mathematischer und physikalischer Struktur. Je größer die abstrakte Schönheit einer Theo rie, desto größer auch ihr Wahrheitsgehalt. Die innere Harmonie m der Struktur der Materie zu erkennen, d. h.

John Von Neumann And The Foundations Of Quantum Physics

John von Neumann and the Foundations of Quantum Physics PDF
Author: Miklós Rédei
Publisher: Springer Science & Business Media
ISBN: 9401720126
Size: 59.91 MB
Format: PDF
Category : Science
Languages : un
Pages : 373
View: 1928

Get Book

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 Foundations Of Quantum Information And Computation And Its Applications To Nano And Bio Systems

Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano  and Bio systems PDF
Author: Masanori Ohya
Publisher: Springer Science & Business Media
ISBN: 9789400701717
Size: 60.49 MB
Format: PDF, Mobi
Category : Science
Languages : un
Pages : 760
View: 3518

Get Book

This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described.

Spectral Theory And Quantum Mechanics

Spectral Theory and Quantum Mechanics PDF
Author: Valter Moretti
Publisher: Springer
ISBN: 331970706X
Size: 63.34 MB
Format: PDF
Category : Mathematics
Languages : un
Pages : 950
View: 2476

Get Book

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."