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Title: Mathematical Foundations of Quantum Mechanics by John Von Neumann, John Von Neumann ISBN: 0-691-02893-1 Publisher: Princeton Univ Pr Pub. Date: 28 October, 1996 Format: Paperback Volumes: 1 List Price(USD): $39.50 |
Average Customer Rating: 4.29 (7 reviews)
Rating: 5
Summary: Still a classic and one of my favourites
Comment: 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 far (except maybe for Greiner's textbooks, which are considered classics in Germany's QM courses, and Shankar's "Principles of Quantum Mechanics"). We were prescribed Merzbacher's "Quantum Mechanics" in 3rd year and it seemed to lack the mathematical rigour I found in Von Neumann's book. Though written a long time ago (in the 1920s), it is still considered to a good and insightful book on the mathematics underlying the different formulations of QM in those early years (the path integral formulation is not treated here, since it was not yet worked out). It's been a really enjoyable but sometimes challenging read for me, and I won't recommend it to starters on QM, except for those who have a relatively good grounding in Algebra.
Rating: 5
Summary: Hilbert Space Formulation of QM
Comment: 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.
Rating: 4
Summary: Has Strengths and Weaknesses
Comment: 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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Title: Principles of Quantum Mechanics by P. A. M. Dirac ISBN: 0198520115 Publisher: Clarendon Pr Pub. Date: March, 1982 List Price(USD): $55.00 |
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Title: Lectures on Quantum Mechanics by Paul A. M. Dirac ISBN: 0486417131 Publisher: Dover Pubns Pub. Date: March, 2001 List Price(USD): $6.95 |
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Title: Physical Principles of the Quantum Theory by Werner Heisenberg ISBN: 0486601137 Publisher: Dover Pubns Pub. Date: December, 1930 List Price(USD): $9.95 |
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Title: Quantum Theory by David Bohm ISBN: 0486659690 Publisher: Dover Pubns Pub. Date: June, 1989 List Price(USD): $18.95 |
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Title: Calculus of Variations by S. V. Fomin, I. M. Gelfand ISBN: 0486414485 Publisher: Dover Pubns Pub. Date: November, 2000 List Price(USD): $9.95 |
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