Quantum Mechanics in Hilbert Space (Pure and Applied Mathematics): Eduard Prugovecki (Repost)

Description

Review:
If you're looking for a book talking rigorously about the mathematical foundations and the formalism of quantum mechanics, this is the one you were after.

Perhaps you've encountered lack of rigor in presentatoin of QM in standard physical textbooks. Sometimes it's not harmful and the theory can survive. But there are plenty of cases for which the presented formalism by physicists, though useful in dealing with many problems, turns out to be absolutely wrong and even leading to logically wrong conclusions.

This book presents you with a rigorous, well established formalism of QM, arising from the very fundamental roots of the theory in functional analysis and Hilbert space.

There is at least one advantage: making you sure that QM is logically correct and works. But through learning this point, one underdstands that what really works is not exactly what one encounters in standard physics textbooks. Another benefit is of course to learn pretty theories of Hilbert space, measures and operators. A disadvantage, for a physicist like me, is the lengthy proofs; okay, ignore them and just study the propositions themselves quite rigorously.

I think it's worth having the book as a source for many mathematical theories and a nice perfect approach to QM.

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