Amazon.com: Customer Reviews: An Introduction to Quantum Theory
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on August 29, 2010
I don't know why this wonderful textbook does not get more attention. Levin is more detailed and more formal than other introductory QM texts I have studied, e.g. Miller Quantum Mechanics for Scientists and Engineers (Classroom Resource Materials), Townsend A Modern Approach to Quantum Mechanics, Das/Melissinos Quantum Mechanics: A Modern Introduction or poked my nose into online at Amazon or google books, e.g. Griffiths Introduction to Quantum Mechanics (2nd Edition), Zettili Quantum Mechanics: Concepts and Applications. I would personally classify it as an intermediate text, at least from the perspective of self-study, because the demands on the reader are substantial. It really is meant for serious students who want more quantum mechanics under their belts than provided by typical standard introductions. Because of its substantial breadth and depth, it's also a good reference and a useful supplement to other textbooks. The exposition is very clear. For very dedicated autodidacts, it is eminently suitable for self-study (but note that there are no solutions to exercises).

As one reviewer notes, the first 5 chapters are somewhat ponderous; in fact, I skipped them at first and then went back to them later, but I had already read most of Miller and Townsend and some other material on the formal foundations of Hilbert spaces and QM, e.g., some of Shankar Principles of Quantum Mechanics; cf. my other reviews and ListMania.

Here's the early chapter roster:

Ch. 1: The Need for a Non-classical Description of Microscopic Phenomenon (pp. 1-26);

Ch. 2 Classical Concepts and Quantal Inequivalences (pp. 27-45);

Ch 3. Introducing Quantum Mechanics: a Comparison of the Classical Stretched String and the Quantal Box (pp. 46-83);

Ch. 4 Mathematical Background (pp. 84-128);

Ch. 5 The Postulates of Quantum Mechanics (pp. 129-173).

Only then in Ch. 6 (Applications of the Postulates: Bound States in One Dimension) does one get into the nitty gritty of some interesting quantum physics.

Nevertheless the introductory first 5 chapters are very well written, very informative and well worth the effort of reading if one is unfamiliar with this material. I came away with a much better understanding of various fundamentals.

Levin covers a number of topics that in other introductory books are either ignored or treated inadequately. For example, section 3.4 (The concept of Hermiticity) discusses the Sturm-Liouville operator in some detail and its relationship to the Dirac delta function; section 4.5 Functions of operators provides a serious discussion of unbounded operators, including Stone's theorem; and Ch 8.2 provides an introduction to the path integral formulation of QM.

Overall, very highly recommended for the dedicated autodidact.
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on July 15, 2004
Levin's undergraduate book is very complete. A course like this would be an excellent foundation for a graduate course later on. If you've ever looked at gasiorowicz, which is also quite complete, it's like that plus all the words/explaination that G-wicz is missing. I highly recommend this book.
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on April 23, 2010
I wasn't in the market for a quantum book, but happened to pass by this one at the store, and had to get it. First off the book is beautiful. They have done a great job making the text clear and visually comfortable, the equations read beautifully, and the book "feels" light for being over 700 pages (big pages).

Topic wise the book is very thorough. Both in the sense of many topics are covered and they are generally covered thoroughly and formally. I really think Levin does a great job of balancing rigor with clarity. Although I haven't made it all the way through the text, I've peeked ahead to several sections and been impressed with content. Likewise I haven't sat down with the pencil and paper and worked out the problems, but the problem sets I read through looked polished.

As far as complaints go, I've have a couple, generally mild -- ok this first one is actually pretty picky. The author uses the phrases "vis." and "quantal" all of the time. After a couple of days it became less annoying, but now I find myself saying quantal from time to time -- almost like getting a song stuck in your head.

The other complaint isn't really on my behalf, but on the behalf of a first time student. I think many of the early chapters don't get to "it" quick enough. The basic 1-d problems aren't really attacked until chapter 6, page 175. Everything before that provides motivation and formalism. I think that may be a little too far of a lead-in for the uninitiated student, so if its used in a intro QM class, the teacher probably shouldn't strictly follow the text's path.

Otherwise this book if fantastic. It goes above and beyond the content needed for a first year course, while keeping that content accessible. I think this text has more than will be swallowed by most first year undergrad classes, and could probably be used by many universities graduate QM classes. It's been several years, so I won't directly compare this to the texts I used, but even if you aren't assigned this text, I would recommend picking it up as a reference (especially if you are an undergrad using say Griffiths, who is looking to continue into grad school).
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on November 24, 2011
If you've been looking for THE quantum theory book for undergraduate studies, say "bingo" because you just found it. Some pretty serious problems in there, it'll satisfy all you people looking for challenges.
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