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Rating: 
Summary: read a Lie groups math book FIRST
Review: Book: Quantum Mechanics - Symmetries, 2nd edition, 15 chapters, 496 pagesScope of the book: applications of group theory in elementary particle physic (no field theory!) Reader: PhD student in physics, I am a beginner in that area, this is my first book in symmetries and Lie groups. My evaluation:
The math sections in the book give u some basic notion of Lie groups but are NOT sufficient to fully understand the logic behind the scene everywhere. My advice is to read some good book in Lie groups in advance.
The strongest feature of the book is its richnes of examples and solved exercises both in group theory and in its application to particle physics. You can learn a lot of analytical 'tricks' from the solutions.
At the same time the text is full of small errors (signs, indexes, equation numbers, misprints). They are easy to detect and fun to debug and keep you concentrated while debugging.
My main objection is that very often the logic in the text remains hidden, broken or fuzzy. Sometimes they prove some statement but at the end you can't tell what was actually proven or under what conditions that proof is valid, what facts it is derived from, does it rely on implicit assumptions or it's generaly true. As a consequence of that you are not sure if you can apply the statement for a situation that is not exactly the one discussed in the book. Sometimes it's hard to tell if they are talking about a necessary of sufficient condition or both. Or they, having something in mind that you don't know about, make some sudden assumption and you wonder why (example: equation (13.3) on page 442 assumes that the parity transformed wave function is proportional to the old one. why? cause they assume implicitly without stating it that parity commutes with the Hamiltonian, hence they have common eigenfunctions). Some concepts are not defined sharply from the begining but instead the authors use fussy definitions and define them much later (example: tensor product of multiplets and its reduction is defined understandably in chapter 10 but is used all the time before that). The explanations of the algebra in the examples and exercises is also not the best since in many cases I see a more logical, organized and understandable way to explain it to the reader. Also in some cases the book gives just the algebra without giving the reader the more fundamental cause for some fact(example: in exercise 8.3 page 255 they have two matrices connected by a similarity transformation, they prove with some algebra that the eigenvalues remain the same but don't tell you that's always the case with similarity transformations). To my opinion the authors have to a lot of work to do to make the logic structure of the text (the connections between different statements,the difference between assumptions and derivable facts) fully explicit and understandable to the reader everywhere in the text. Without that, the book can be regarded as a nice collection of solved examples and exercises in group theory and particle physics. I give that book 3 out of 5 stars and hope that the other volumes of the sequence don't have that flaw. Contents of the book: chap1: symmetries in classical physics, Noether's theorem, symmetries in quantum mechanics and their generators: momentum, angular momentum, energy and spin operators chap2: angular momentum algebra; irreducible representations of SO(3); addition of angular momenta; Clebsh-Gordon coefficients
chap3: Lie groups, generators, Lie algebra; Casimir operators and Racah theorem; multiplets;
chap4: enumeration of the multiplets through eigenvalues of Casimir operators; energy degeneracy within a multiplet; two or more commuting symmety groups
chap5: neutron, proton doublet; isospin SU(2) symmetry; pion triplet; adjoint representation of Lie algebra
chap6: charge Q; hypercharge Y; baryons, antibaryons, baryon resonances; T3-Y diagrams;
chap7: U(n) and SU(n) groups; generators, Lie algebra of SU(3); subalgebras of SU(3) and shift operators; dimensions of SU(3) multiplets D(p,q);
chap8: smallest non-trivial representations of SU(3), quarks; meson multiplets; tensor product of multiplets and their reduction; Gell-Mann-Okubo mass formula; quark models with spin added, SU(6); wave functions construction, proton, neutron, baryon decuplet, baryon octet; mass formula in SU(6);
chap9: permutation group Sn, identical particles; Young diagrams; dimensions of irreducible Sn representations; connection to SU(n) multiplets; dimensions of SU(n); decompositions of SU(n) multiplet into SU(n-1) multiplets; decomposition of tensor product of multiplets with Young diagrams;
chap10: group characters; schur first and second lemma; orthogonality relations of characters of discrete finite groups; reduction of reducible representations; continuous, compact groups, group integration; integration over unitary groups; group characters of U(n); quark-gluon plasma example;
chap11: charm, SU(4), group generators; smallest non-trivial representations of SU(4), [4] and [4bar]; decomposition of tensor products of SU(4) multiplets; OZI rule for suppressing reactions; meson and baryon multiplets, SU(3) content; potential model of charmonium;SU(4)[with spin SU(8)] mass formula;
chap12: weight operators, standard Cartan-Weyl basis of a semi-simple Lie algebra; root vectors; graphic representations of root vectors and Lie algebras; simple roots and Dynkin diagrams;
chap13: space reflection (parity); time reversal; antilinear operators, complex conjugate operator K, antiunitary operator; general form of time reversal operator in coordinate representation for particle with spin;
chap14: classical hygrogen atom constants of motion: energy, angular momentum, Runge-Lenz vector; corresponding quantum constants of motion (operators), their algebra and group SO(4)- dynamical symmetry; decoupling of the SO(4) algebra into two SO(3) algebras and determination of the energy eigenvalues (Pauli method i guess); classical and quantum isotropic oscillator;
chap15: compact and noncompact Lie groups; group SU(p,q); group SO(p,q); generators of SO(2,1), infinitesimal operators, Casimir operators; non-compactness of SO(2,1) and its infinite dimensional irreducible unitary representations; application of SO(2,1) representations to scattering problems;
Rating: 
Summary: One of the best Textbooks on non relativistic QM
Review: I've read all the 3 Greiner's books concerning non relativistic Quantum Mechanics (and other on QFT). First I've to underline that you may find many text-errors in those books. (QM: an introduction, QM:Special Chapters, QM:Symmetries): for everybody who is a bit familiar with Mathematics this can not be a big problem. On the second hand, you have to read all the 3 Greiner's books on Q.M. to have a great overview on this matter: every mathematical part is essential but complete. One has to follow and understand most of the calculations inside: this is the only way, generally in Physics, to earn a good Mathematical level, and be able not to concentrate too much on Mathematics while trying to understand the Physics behind. As last point I've to underline that only by reading Greiner's "Relativistic Quantum Mechanics" book, one is able to understand the meaning of introducing Field Theory formalism in "Q.M.:Special Chapters" and will appreciate it a lot: in fact everything is going to be easier on the following matters; apart of this I think it's great to treat Statistical Mechanics with operators as soon as possible, as Greiner does in Q.M.:special chapters. Lot's of importance is given to symmetries and Group theory (Q.M:symmetries) as a modern point of view pretends.
Rating:
Summary: One of the best Textbooks on non relativistic QM
Review: I've read all the 3 Greiner's books concerning non relativistic Quantum Mechanics (and other on QFT). First I've to underline that you may find many text-errors in those books. (QM: an introduction, QM:Special Chapters, QM:Symmetries): for everybody who is a bit familiar with Mathematics this can not be a big problem. On the second hand, you have to read all the 3 Greiner's books on Q.M. to have a great overview on this matter: every mathematical part is essential but complete. One has to follow and understand most of the calculations inside: this is the only way, generally in Physics, to earn a good Mathematical level, and be able not to concentrate too much on Mathematics while trying to understand the Physics behind. As last point I've to underline that only by reading Greiner's "Relativistic Quantum Mechanics" book, one is able to understand the meaning of introducing Field Theory formalism in "Q.M.:Special Chapters" and will appreciate it a lot: in fact everything is going to be easier on the following matters; apart of this I think it's great to treat Statistical Mechanics with operators as soon as possible, as Greiner does in Q.M.:special chapters. Lot's of importance is given to symmetries and Group theory (Q.M:symmetries) as a modern point of view pretends.
Rating:
Summary: QM for advanced larner.
Review: Probably for most of the people it is better to start QM with easier books, e.g., Landou. Greiner's physics series are little more sophisticated, and may be difficult for someone with poor math background. For someone who has strong math background, Greiner's books are fun to read even without any physics background. With your strong math background, you can learn a lot out of this text.
Rating:
Summary: Excellent text of quantum mechanics
Review: There is nothing better than this book. This is a part of Walter Greiner's theoretical physics. German edition of this series have been sold a million and this English edition is a tranlation of German 5th edition. Translation is a difficult job. I also found many typos and incorrect translations but it did not interrupt my understanding on the subject. This book contains carefully worked examples and enough mathematical insight. It is very nicely written. This is one of the most elegant mathematical physics text.
Rating: 
Summary: The publisher and authors should be ashamed of themselves
Review: This book could be one of the most useful books on the use of symmetry in quantum mechanics; but it is so filled with typographical errors that it is impossible to read. There are 75 serious errors in the first 100 pages. after that i gave up.
Rating:
Summary: quantum mechanics symmetries
Review: This is the most stupid book that I have ever seen. The main concepts of Elementary Particles Theory are introduced before the Quantum Field Theory has been developed. Without knowing Dirac's equation how on the Earth is possible to grasp the intricasies of Modern Physics? Lee groups are not introduces properly either -- the level of mathematical discussion is very low. For all of you who wants to use comprehensive series on Modern Physics I recommend the old ones by Landau and Lifshitz.
Rating:
Summary: full of useful mathematical tools.
Review: this volume is not only useful for understanding non-relativistic quantum mechanics but also it is filled with mathematical tools that is useful in many science and engineering analysis. symmetry of the operators plays always an important role in simplifying the analysis of formidable coupled equations. i found this volume very useful in many ways.
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