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Mathematical Foundations of Quantum Mechanics (Princeton Landmarks in Mathematics and Physics), by John von Neumann
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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.
- Sales Rank: #2521958 in Books
- Published on: 1955-03-21
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 6.25" w x 1.25" l,
- Binding: Hardcover
- 464 pages
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
From the Back Cover
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.
Most helpful customer reviews
0 of 0 people found the following review helpful.
Very satisfied!
By Helen New Zealand
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. He also received it within a week after purchasing from the USA .
So very satisfied !
15 of 17 people found the following review helpful.
Very nice historical approach
By Alex Monras
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.
6 of 6 people found the following review helpful.
Hilbert space based development of quantum mechanics culminating in an assessment of the hidden variables enigma
By Ulfilas
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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