Mathematical Foundations of Quantum Mechanics [Paperback]

John von Neumann (Author)

Book Description

ISBN-10: 0691028931 | ISBN-13: 978-0691028934 | Publication Date: October 28, 1996 | Edition: Translation - from German

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.

Editorial Reviews

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 Details

• Paperback: 464 pages
• Publisher: Princeton University Press; Translation - from German edition (October 28, 1996)
• Language: English
• ISBN-10: 0691028931
• ISBN-13: 978-0691028934
• Product Dimensions: 9.2 x 6.1 x 1.1 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Average Customer Review: 4.3 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #456,626 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

28 of 30 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.

13 of 15 people found the following review helpful:

4.0 out of 5 stars Very nice historical approach, February 1, 2000

By 

Alex Monras (Barcelona) - See all my reviews

This review is from: Mathematical Foundations of Quantum Mechanics (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.

11 of 13 people found the following review helpful:

5.0 out of 5 stars Hilbert Space Formulation of QM, April 10, 2003

By 

"zamanian" (USA) - See all my reviews

This review is from: Mathematical Foundations of Quantum Mechanics (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.