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Mathematical Foundations of Quantum Mechanics [Paperback]

John von Neumann (Author)

4.4 out of 5 stars See all reviews (8 customer reviews)

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Product Details

Paperback: 464 pages
Publisher: Princeton University Press; Reprint edition (Oct 28 1996)
Language: English
ISBN-10: 0691028931
ISBN-13: 978-0691028934
Product Dimensions: 23.3 x 15.5 x 2.8 cm
Shipping Weight: 680 g

Average Customer Review: 4.4 out of 5 stars See all reviews (8 customer reviews)

Amazon Bestsellers Rank: #2,306 in Books (See Top 100 in Books)
- #1 in Books > Professional & Technical > Professional Science > Mathematics > Mathematical Physics
- #1 in Books > Science > Mathematics > Mathematical Physics
- #2 in Books > Computers & Internet > Programming > Introductory & Beginning > Computer Dictionaries

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Review

It remains indispensable to those who desire a rigorous presentation of the foundations of the subject. -- "Quarterly of Applied Mathematics

The translator and publisher have performed a service in making the classic available to a wider circle of English-speaking readers. It remains indispensable to those who desire a rigorous presentation of the foundations of the subject. -- A. F. Stevenson, Quarterly of Applied Mathematics

Product Description

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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Front Cover | Copyright | Table of Contents | Excerpt | Back Cover

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Customer Reviews

8 Reviews

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Average Customer Review

4.4 out of 5 stars (8 customer reviews)

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1 of 1 people found the following review helpful

4.0 out of 5 stars Has Strengths and Weaknesses, July 29 2002

By A Customer

This review is from: Mathematical Foundations of Quantum Mechanics (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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1 of 1 people found the following review helpful

2.0 out of 5 stars generally unedifying, Jan 1 2000

By A Customer

This review is from: Mathematical Foundations of Quantum Mechanics (Paperback)

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 of Hilbert space. Despite the historic significance of the book in establishing a rigorous foundation for the math underlying QM, it is not a good text for developing either a conceptual or functional understanding of modern mathematical techniques in QM.

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5.0 out of 5 stars A still relevant classic, Nov 3 2003

Filippo Neri (Los Alamos, NM) - See all my reviews
(REAL NAME)

This review is from: Mathematical Foundations of Quantum Mechanics (Paperback)

Not just relevant to the history of physics, this great book is still central to the contemporary discussions on the interpretation of Quantum Mechanics. The early chapters provide a discussion of the Hilbert Space formalism. Nowadays this is better explained in (for instance) Chris J. Isham's lectures on Quantum Theory. But the core of the book is the no-go theorem of chapter 4. Bell's inequalities, the Kochen-Specher theorem, etc. are just pedestrian restatements of von N's no-go theorem: only the deluded (or ignorant) can still think there is any way back from Quantum Strangeness, in term of "hidden variables" or anything else!

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Most recent customer reviews

5.0 out of 5 stars Still a classic and one of my favourites
This book contains a rigorous treatment of the mathematical foundations of the Hilbert Space formulation of Quantum Mechanics, unmatched by no other QM book I've come across so... Read more

Published on May 16 2003 by ncr

5.0 out of 5 stars Hilbert Space Formulation of QM
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. Read more

Published on April 10 2003 by zamanian