Quantum Mechanics in Hilbert Space: Second Edition (Dover Books on Physics) by Eduard Prugovecki | (PDF) Free Download

Description

A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas.This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the gap between strictly physics- and mathematics-oriented texts on Hilbert space theory as applied to nonrelativistic quantum mechanics. Organized in the form of definitions, theorems, and proofs of theorems, it allows readers to immediately grasp the basic concepts and results. Exercises appear throughout the text, with hints and solutions at the end.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a long book (685 pp.) and I probably won’t read it cover-to-cover, but it is excellent as a reference, and for reviewing selected topics. Example: reading about spectral measures in another book (Fano, Mathematical Methods of Quantum Mechanics), I needed a proof that partial ordering of projection operators by set inclusion is equivalent to ordering by operator norm. I quickly found in Prugovecki a section on “Partial Ordering of Projectors” that had exactly what I needed. Use as a reference is facilitated by a detailed table of contents and an index of notation. Unlike some of the more mathematical texts on this subject, the book interleaves physical applications with the math, and uses Dirac’s notation throughout.

⭐The author is not a well-known master, but he is a thorough and even elegant expositor. Galois was wrong to say “Only study the masters.” This books is a carefully developed exposition of von Neumann’s approach in his masterful 1932 book. Von Neumann’s book is quite readable, although the typeface is awful and the book is not well written. I like this exposition a lot.

⭐I haven’t read through the whole book yet. Our quantum teacher recommend this book to us, I provides sufficient rigor for serious students of QM. Of course this is not a book for beginners and sufficient undergraduate analysis is helpful.

⭐I wrote this to offset the only other review of this book which I thought was unfair. If you are interested in learning quantum PHYSICS, then this is not the book for you. However, if you are interested in learning the underlying mathematical principles of Hilbert space as applied to QM in a semi-rigorous fashion, then this is a very good book. It reviews the relevant techniques from analysis such as spectral theory and does a good job on formalized scattering theory. I probably would have given it four stars if I was being completely unbiased. I liked it.

⭐Read this about 20 years ago, so bear with me. What I remember, it has some neat mathematical tricks to teach you, but for the title, I would expect it to delve more profoundly into the physics behind completeness of a Hilbert space and what it means for the physical world. It’s probably an OK book, but not something that will let you have a revelation or breakthrough. And as one of the founders of group theory and “revolutionaire extraordinaire” (Evariste Galois) said, “study (only) the masters”- so hard these days when mediocrity and marketing guys rule.

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