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Group Theory in Quantum Mechanics: An Introduction to Its Present Usage (Dover Books on Physics): Volker Heine

This text introduces research students in physics and chemistry to the three main uses of group theory in quantum mechanics. It requires a previous course in quantum theory, but matrix algebra appears in an appendix. A series of examples of varying levels of difficulty follows each chapter. 1960 edition.

Review:

This is my first book on group theory and its applications to physics. I did take a one semester course on algebra in mathematics department when I was an undergraduate, so that I knew the basic properties of groups before reading this book. In my opinion, this is a very good introduction to teach physics students or physicists how to use the group theory in QM. Most of books with a similar title strat with the basic theory of groups and then its applications to physical problems. That is, mathematics first, then physics. This book, however, takes a different philosophy. It tightly binds the mathematics of the group theory with QM at the begining and Keeps the style at later chapters, so that a person who is familiar with QM at the level like ``Principles of QM" by Shankar can absorb the materials which Dr. Heine tried to talk easily. Moreover, at the end of each section, there are a few problems to test your understanding. The proofs of the theorems are put at the appendix such that the main discussions will not be interrupted. The whole presentation is particluarly useful for a person who is not mathematically minded and has no ideas about this topic before. The prerequisites for understanding this book is the mathematics and physics contained in Shankar's QM. After finishing this book, you may consult Cornwell or Gilmore for more complete mathematics and Georgi for the applications of Lie algebra to particle physics. I cannot recommend this book to beginners majoring in physics too highly.

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