This book is a text for an advanced course in quantum mechanics and, indeed, started out as notes for a graduate course at UCLA. Usually students in any field of physics must study quantum mechanics at this level before undertaking more specialized subjects.
The first part covers some of the formalism of quantum mechanics, especially the mathematics of rotations and other symmetries. It begins with a brief review of the Hamiltonian formulation of classical mechanics, which has become a trustworthy guide to finding the form of the quantum rules. The second chapter explains how the canonical quantum rules follow from the superposition principle and some form of the correspondence principle. It ends with the Schrodinger equation and the uncertainty principle.
The third chapter is about stationary states and the energy eigenvalue problem, with particular emphasis on spherical symmetry. It includes the theory of orbital angular momentum and the famous hydrogen atom problem. The latter will serve as a wonderful example over and over again.
The next two chapters are about the role of symmetry transformations in quantum mechanics, and how they restrict the possible values of some observables. There is a detailed discussion of three-dimensional rotations, the general theory of angular momentum, addition of angular momentum and selection rules. A good understanding of rotations in quantum mechanical systems is important for what follows. Rotations are an example for all sorts of other symmetries we have discovered or invented. The techniques learned in this context can be recycled many times.
These first five chapters contain the mathematical foundation of our subject. I have tried to be fairly rigorous, understanding that this is the students' second course in quantum mechanics