Advanced Quantum Mechanics

Rating:
Summary: Solid Book
Review: i'm interesting cost is about 50-60 $ of the Advanced Quantum Mechanics by J. J. Sakurai.

Rating:
Summary: Good for you...
Review: If you're reading reviews on advanced QM then I'm sure you'd like this book... as for me, I'm through with physics. Undergrad stuff is a breeze but it's not worth it anymore. Don't you guys have lives other than physics? Christ, I want time to take a vacation now and then and to watch baseball games and movies and follow current events. I'd like to spend some time with members of the opposite sex every now and then also and make better money than a grad student/research professor for doing the same or less amount of work. This advanced [stuff] requires one to study as a full time job. Good book though and it's a great bridge from his basic QM graduate level text to QFT for those who enjoy studying in their free time.

Rating:
Summary: Not the best text
Review: Most of the graduate students in physics and chemistry here at Cal agree that this book is incomplete and glosses over too much of the details. It's also very annoying to read things like, "Proof: The proof is trivial." Anyone studying from this text will be left with the feeling that something is missing. Personally, I prefer the classic two volume "phonebook of quantum mechanics" by Cohen-Tannoudji et al.

Rating:
Summary: Difficult book, for grad student but it rewards time spent.
Review: This book certainly isn't for the casual reader, but it is a great book for those who want to learn Advanced quantum mechanics and quantum electrodynamics from a distinguished physicist from a different point of view. Sakurai interjects his own beautifully strange and humourous analogies through out the work, such as comparing the creation, anihilation and number operators to the hindu trinity of Brahma, Siva and Vishnu respectively. Again there are some people who don't get this book, yet there are others who love it.

Rating:
Summary: Horribly terse
Review: This book is great - until you try to do the problems. I'm slightly peeved, having spent upwards of 30 hours (working with other grad students!) and not 'completely' got any of the 6 assigned problems from the back of Chapter 2.

Oh, this book fills a gap between quantum and QFT to be sure. And it's one of the only books (the only?) that does it. What this means is that if you don't understand it here there aren't any other books you can look up. Gordon Baym comes close, but falls short and is out of print.

Over the past 30 (non-continuous) hours, I've come to greatly detest Sakurai's style (even more than when we were using 'Modern QM' for the beginning of this sequence). For some 'simple' problems, it's 'fun' that he doesn't fill in all the steps so you have to read the book in detail and re-derive the relevant steps. But as the problems get more involved and you still 'don't get it' after reading the chapter 4 or 5 times, the whole thing just ceases to be entertaining.

While the *mathematical* tools to do the problems are probably all in the text somewhere, Sakurai simply does not provide the 'cut through the mathematical [stuff] and get to the physics' insights that are necessary to truly understand and utilise the material. This is not to say that the treatment isn't 'physical' at times and in homeopathic quantities, but Sakurai doesn't do much to tie different ideas together andgive one the big picture.

Bottom line: Mr. Sakurai, paper is cheap. Use more words. Please.

Rating:
Summary: Good for you...
Review: This book represents to a large degree an approach to quantum field theory that is now viewed as somewhat out of date. Modern textbooks and monographs in quantum field theory emphasize functional methods, the renormalization group, the operator product expansion, and topological field configurations. In addition, this book was published before the advent of the electroweak theory, and so readers will not get an introduction to this theory, nor to quantum chromodynamics, the gauge theory of the strong interactions. The only gauge theory actually treated in the book is quantum electrodynamics, although the author does not exploit the gauge invariance of this theory to its fullest potential in the book.

For those readers who want learn quantum field theory, this book would probably not suffice, due to the above omissions. However, the book might still be used as a reference, and one that, as stated by the author, emphasizes the physics of quantum field theory. Covariant perturbation theory and Feynmam diagrams are given ample treatment. In addition, the author does not hesitate to employ symmetry considerations in the discussion of the transformation properties of the Dirac wave function and the quantized Dirac field. The spin-statistics theorem is not proven, but some plausible arguments as to its validity are given, dealing with the difficulty in constructing a quantum field theory for the electron that does not obey the Pauli exclusion principle. And, as another example of the avoidance of complicated mathematics, the author chooses to discuss the Moller interaction between two electrons using the (noncovariant) Coulomb gauge. In this strategy, the transverse part of the vector potential is treated dynamically, and the electron interaction consists of the interaction of the transverse electromagnetic field with the Dirac current and the instantaneous Coulomb interaction between charge densities. Only the transverse part of the vector potential is quantized, but interestingly, the nonphysical, longitudinal parts cancell out in the calculation of the amplitude. This approach may be distasteful from a modern gauge-invariant point of view, but it does suffice to bring out the physics of the problem, and it does serve to motivate the modern approach to the calculation of the Moller cross-section.

Thus, this might still serve to build insight into the physics of quantum field theory. Too often modern texts emphasize the mathematical formalism, the latter becoming more and more formidable as the years go on. The chapter on covariant perturbation theory is definitely worth some amount of time because of this. The reader can then move on to the magnificent fortresses built by the theoreticians of quantum field theory since this book was published. Quantum field theory is definitely still a very active subject, and there are lots of things in the theory that remain unsolved to this day.

Rating:
Summary: Very good introduction to quantum electrodynamics
Review: This is a very fine book on quantum electrodynamics and should not be confused with Modern Quantum Mechanics, which is a postumous text on quantum mechanics, too formal to my taste. Advanced Quantum Mechanics, on the other hand, is quite the opposite. The treatment of field quantization is very intuitive, based on Fermi's ideas, and Physics is always kept to the forefront. Calculations (there are plenty of them; this is not a couch book) are very detailed and, alas, must be redone with much attention, for typos are quite frequent. I believe this to be still the book to be recommended for a beginner. She should, after all, know the physics, and be able to do a back-of-envelope estimative of the size of Lamb shift, by Bethe's method. The book teaches you that.

Rating:
Summary: Intermediate Quantum Mechanics
Review: This textbook cannot be considered an advanced Quantum Mechanics (QM) book. It really is an intermediate QM book, useful to bridge the gap between a nonrelativistic QM textbook (Ballentine, Sakurai, Cohen-Tannoudji...) and a full-blown Quantum Field Theory book (Weinberg, Itzykson-Zuber...). In this role, basically it is the only choice.

All the complaints of other reviewers are true: this book is very terse and sloppy. The problems are too hard. The convention for the Dirac gamma-matrices is not the one prevalent today.

However, even with all these problems, this book is still necessary. The discussion of the EM field quantization in the radiation (Coulomb) gauge is essential for applications to atomic and molecular physics.

Also, the inconsistent notation problem is endemic to theoretical physics: one has to be able to handle it, to be a professional physicist! Use this book for practice.

The other intermediate QM book is the one by Bethe and Jackiw: it is much better for atomic and molecular physics, but it lacks a chapter on the quantization of the EM field. So one still needs this book.

Rating:
Summary: Lacking Physical Insight
Review: This textbook gives a rather formal treatment of quantum mechanics. That is not to say that it is in a theorem-proof format like Neumann, for example, but still I find it lacking actual physical context: the author gives too much emphasis to algebraic derivation as means of explaining basic concepts.

Personally, I find Landau much more enlightening (if, as students often complain, harder to read). I would suggest to use these two books as complementary to each other: Sakurai for its clarity and Landau for its physics.

My other favorite, at a more introductory level, is Shankar, for it is very physical and very easy to read.