Mathematical Foundations of Quantum Mechanics 1st Edition

by John von Neumann (Author), Robert T. Beyer (Translator)

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ISBN-13: 978-0691028934

ISBN-10: 0691028931

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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.

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Product Details

Series: Princeton Landmarks in Mathematics and Physics
Paperback: 464 pages
Publisher: Princeton University Press; 1st edition (1955)
Language: English
ISBN-10: 0691028931
ISBN-13: 978-0691028934
Product Dimensions: 6 x 1 x 9.2 inches
Shipping Weight: 1.5 pounds (View shipping rates and policies)
Average Customer Review: 4.4 out of 5 stars See all reviews (10 customer reviews)
Amazon Best Sellers Rank: #1,051,269 in Books (See Top 100 in Books)
- #715 in Books > Science & Math > Physics > Mathematical Physics
- #963 in Books > Science & Math > Physics > Quantum Theory
- #2717 in Books > Textbooks > Science & Mathematics > Physics

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Has Strengths and Weaknesses

ByA customeron July 29, 2002

Format: Paperback

First the strengths:
(1) The author gives a rigorous proof of the incompatibility of the two theories of quantum mechanics, that is, the evolution of the state vector as determined by Schrodinger's equation and the collapse of the state vector by means of an observation. He does this by the concept of entropy.
(2) He gives a thorough treatment of the "consciousness school" of interpretation, which makes for an interesting,if not entirely convincing read.
The weaknesses:
(1) the font is a pain to read; it looks like it came off an old typewriter. I wonder why the publishers couldn't put it into a more modern readable form.
(2) Von Neumann writes this book , in part, with the intention to dispel the mathematical nonsense, as he perceives it, of the Dirac delta function. Therefore he casts everything into the unwieldy formalism required to do without the distribution. Indoubtedly he was trying to change the dirac formalism in use in quantum mechanics at the time but was fortunately unsucessful in persuading physicists to use his alternative language.
Summary: I recommend this book for anyone wishing to deepen his or her understanding of the foundations, conceptual and mathematical of quantum theory.

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Very nice historical approach

ByAlex Monrason February 1, 2000

Format: Paperback

This is not the kind of book I would recommend to a novice person in the area, but it does give a very interesting view of how was quantum mechanics born. It begins with a thorough discussion about the mathematics of Hilbert spaces and operator theory to later merge Heisenberg's and Schrodinger's theories in one rigorous mathematical theory. It makes some remarks that allows the reader to see how was the 'new' quantum theory born and developed, since it briefly discusses the theories of Heisenberg and Schrodinger in the way they originally stated them. Maybe the most disturbing issue would be the notation since in 1932 dirac had still not developed the bracket formalism.

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Hilbert space based development of quantum mechanics culminating in an assessment of the hidden variables enigma

ByUlfilason February 26, 2012

Format: Paperback

It is always exciting to read a book written by one of the founders of a discipline. There could nothing more "straight from the horse's mouth" than John von Neumann's treatment of quantum mechanics in terms of Hilbert space--especially since von Neumann was a student of Hilbert at Gottingen--the epicenter of world mathematics in the 1920's and early 1930's. The only way you could have a more authentic experience would be to read this book in the original German. it is also worth noting that von Neumann's book is famous for its treatment of the hidden variables enigma in quantum measurement.

Von Neumann's mathematically intense development of quantum mechanics in terms of Hilbert space includes a statistical treatment involving such concepts as the Stieltjes Integral. Some familiarity may be gained regarding this and other statistical devices used by von Neumann from the online statistics text book "statlect" written by Marco Taboga, who is senior economist at the Bank of Italy. Better yet, as pointed out by another reader, is Hughes' excellent introductory book The Structure and Interpretation of Quantum Mechanics provides the reader with much of what he needs to understand von Neumann's treatment. Hughes provides the reader with the equivalent of a B.S. in physics a lucid and accessible introduction to Hilbert space in quantum mechanics. Other excellent Books addressing quantum mechanics in terms of Hilbert space at the level accessible to first year graduate students include Guido Fano's Mathematical methods of quantum mechanics and T. F. Jordan's Linear Operators for Quantum Mechanics (Dover Books on Physics).

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Hilbert Space Formulation of QM

ByAmazon Customeron April 10, 2003

Format: Paperback

The ultimate source of Hilbert Space applied to Quantum Mechanics. John von Neumann was the first to systematically formulate QM in such a powerful and elegant vector space. If this is the Bible of QM in HS, Hughes is the missioner! Get the book as well -- The Structure and Interpretation of Quantum Mechanics.

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A must-own for any quantum mechanic affectionado

ByNova137on January 20, 2013

Format: PaperbackVerified Purchase

John Von Neumann towers as one of the great mathematicians. Said by some to possess skills exceeding normal human capabilities, he was able to contribute to many different areas of science and engineering, including computer systems theory, set theory, functional analysis, and statistics. He also contributed immensely to the field of quantum mechanics.

This book represents that immensity. Covering the development of the Transformation Theory and its origin to the Measuring Process, von Neumann is capable of providing the mathematical rigor as well as detailed and easy to understand commentary throughout this important work.

The Notes in this work stand out, especially. They are informative and compliment the main text explicitly, expanding it and making it more informative. They often go beyond a simple reference to operate as a subtext of the main text, not to be ignored.

Further adding to this point is the fact that von Neumann, throughout this work, continues to give personal commentary: *reasons* for and historical references to, the many mathematical pronouncements and derivations. For instance, on page 196 he begins to develop the statistical assertions of quantum mechanics. By page 198 we have been shown "one of the first and simplest examples by means of which the statistical character of quantum mechanics was recognized." Not only was the derivation clear and concise, the reader is provided the historical context as well.

Often a book of this sort is more a historical document than active reference (unless you are capable of the math). As such, books on quantum mechanics authored by the early founders (and, in this case, a later superb contributor and inventor of notions like "quantum logic") offer an insider look at the mindset of both the classically trained physicist against what the new physical theory asked of that mind.

For instance, this is reflected in a superb Preface, wherein the author states the object of this book ("to present the new quantum mechanics in a unified representation which, so far as it is possible and useful, is mathematically rigorous...what is presumably a definitive form: the so-called "transformation theory."). We also learn in this Preface that "we shall as a rule omit any discussion of the application of quantum mechanical methods to particular problems, as well as any discussion of special theories derived from the general theory - at least so far as this is possible without endangering the understanding of the general relationships."

He goes on to point out that his mathematical treatment in this work "deviates considerably from that of Dirac." Thus, he takes Dirac's "elegant" theory for it "in no way satisfies the requirements of mathematical rigor - not even if these are reduced in a natural and proper fashion to the extent common elsewhere in theoretical physics. For example, the method adheres to the fiction that each self-adjoint operator can be put in diagonal form."

Von Neumann's solution is to start from the beginning with Hermitean operators and Hilbert spaces which "provide the framework" for the Transformation Theory. This book is that story in the authors own voice.

I suggest you purchase a copy for your library today.

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Most Recent Customer Reviews

Very satisfied!

Bought this as a present for my dad. He is very pleased with the quality of the book and he thinks it's very well priced compared to what they have to pay for the same in Europe.Read more

Published 10 months ago by Helen New Zealand

a very elegant book

This is a beautifully written book, more for mathematicians than for physicists, since von Neumann does not really discuss the physics that goes into the subject.Read more

Published on February 20, 2010 by Narada

a classic

As an undergrad, I am sorry that I cannot share the perspectives of professionals as expressed below.Read more

Published on August 23, 2000 by Jihwan Myung

generally unedifying

I strongly recommend perusing a printed copy of this text before deciding upon purchase. A large body of the text consists of mathematical proofs of mostly elementary properties...Read more

Published on January 1, 2000

Quantum Bible

von Neumann's text is still the standard, some 40 yrs after its pub date, for the definitive mathematical treatment of Quantum Mechanics.Read more

Published on November 25, 1999 by Mark Witucke

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