OK, let me start like this. There are many books on quantum mechanics. If I start to list some of the books that I know about then I might say Griffiths, Liboff, Bransden, Townsend, Mcintyre, Golwala, Gottfried, Zettilli, Feynman & Hibbs, Dirac, Greiner, Shanker, Bohm, Landau & Lifshitz, Tannoudji, and Schiff. So, is Sakurai just one of the many books on quantum mechanics? Well, yes, in my opinion, it is one of the many books but all of the books listed above have their positive and negative points and Sakurai is no exception.
First of all, let's look at the eight chapters of the book. In the first chapter, he talks about bra ket formalism (a.k.a the Dirac notation). The second chapter talks about dynamics (and gauge transformations) while the third chapter (one of the most important chapters of the book) is about angular momentum and related techniques. The fourth chapter is about symmetries (parity and time translations in particular) while the fifth chapter (again, a very important chapter) is about the approximation methods (perturbation theory, variational principle, and WKB approximation). The sixth chapter (super important chapter) is about non-relativistic scattering (and it talks about partial wave analysis with many other approximations -e.g. Born approximation- and applications -e.g. applications to nuclear form factor calculations-). The seventh chapter is about the handling of identical particles with applications to the helium atom while the last chapter is about the basics of relativistic quantum theory (a.k.a the Dirac equation).
Now, what are the positive aspects of this book? Well, they are as follows:
1) It uses Dirac notation in almost all of its treatments and thus, the reader gets used to the notation and he/she starts to consider the state as the fundamental thing instead of the wavefunction (David Wallace might not like it 🙂 ). Moreover, he emphasizes the use of unitary operators in Hilbert space. This is very useful to get the concepts straight.
2) Many (almost all) books on quantum mechanics do not consider the case when the degeneracy is not removed in the first order while using the degenerate perturbation theory (by the way, if anyone is interested in the treatment of this case, he/she should see Barton Zweibach's lecture on this case. He treats it very clearly and rigorously). Sakurai is no exception to this statement. However, it gives an exercise in which he talks about this situation.
3) The number (and quality) of exercises provided are very useful and often, very pedagogical.
4) It presents useful methods in the treatment of angular momentum calculations. Most useful is the proof of (and use of) the Wigner-Eckart theorem. This theorem simplifies the problems so much but it is absent from many textbooks on quantum mechanics.
What about the negative points? Here they are.
1) Sometimes (not many a times but sometimes only) this book is not rigorous. The treatment of scattering from the start is not clear enough (although it becomes clear later). The main reason for this absence of rigor is the use of plane waves as the incident and final states (which is a problem independent of this book). The big-box approximation makes things less rigorous and elegant.
2) The same reason makes the treatment of quantization of electromagnetic field very obscure. I think that he shouldn't have included this topic in this book. The proper treatment of the quantization of the electrical field (and even the scalar field) needs quantum field theoretical methods but he is again doing it in the big box approximation with finite volume. That topic is not very helpful in this book (although the derivation of the Casimir effect that he does is very elegant and appealing).
I hope this was helpful. Happy reading.