Mathematical Foundations of Quantum Mechanics

Rating:
Summary: Has Strengths and Weaknesses
Review: As an undergrad, I am sorry that I cannot share the perspectives of professionals as expressed below. After initial introductory courses, I got fascinated by certain untold conceptual issues. And one of the textbooks (probably Griffiths) suggested von Neumann had tried to prove mathematically that the classical formulation is just the furthest the formalism can go and we don't have to worry about underlying complexities. Later, Bohm created a formalism which von Neumann "proves" to be mathematically impossible in this book. I bought this book just to find out how the proof goes. But I got stuck with some tedious proofs on Hilbert space (which he calls a "digression"). This part isn't essential but as the braket notation is not used you need to consult this part. I think at least a strong background in linear algebra is required. Definitly not an introductory textbook. Most useful for those who study history of physics.

Rating:
Summary: A still relevant classic
Review: 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!

Rating:
Summary: Hilbert Space Formulation of QM
Review: 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:
Summary: Hilbert Space Formulation of QM
Review: 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:
Summary: Still a classic and one of my favourites
Review: 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:
Summary: Very nice historical approach
Review: 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.

Rating:
Summary: generally unedifying
Review: von Neumann's text is still the standard, some 40 yrs after its pub date, for the definitive mathematical treatment of Quantum Mechanics. This comes to me from an expert in the field at the U of Chicago. (He also reccomended Dirac's seminal text to those wishing knowledge of the inner workings of Q. M.) Read the Quantum Bible and learn from the very same source from which the experts cut their teeth. Available from Amazon dot product com. and the Seminary Co-op in Chicago 773-752-4381. Mark Witucke Bookseller Chicago