Group Theory and Quantum Mechanics

Rating:
Summary: Should be required for all quantum mechanics students
Review: Even after taking 3 semesters of quantum mechanics, I felt like I had a pretty shaky grasp on topics such as selection rules and the addition of angular momenta. I had heard about the important role that group theory plays in quantum mechanics, so I took a mathematics class in abstract algebra. Though this covered a lot of interesting topics in group structure and ring theory, I was left with almost no idea how the material applied to quantum mechanics. Tinkham's book is invaluable in that it develops the parts of group theory that are extremely relevant to physics and chemistry such as the theory of representations (topics that mathematicians seem bored by) and then shows beautifully how it applies to quantum mechanics. Not only did I understand the selection rules, angular momentum, etc... I had a much better understanding of quantum mechanics overall. Group theory makes much more evident what is meant by "good quantum numbers", where degeneracies come from, and other basic issues in quantum mechanics. Particularly clever was the discussion of the Bloch wavefunction ansatz as a consequence of the Abelian symmetry group of a periodic crystal lattice. Invaluable for quantum chemistry, a subject which is touched on, but which was not nearly as developed when the book was written as it is today. Tinkham knows his math, but he knows his physics even better. If you have any interest in quantum mechanics, get this book!

Rating:
Summary: Should be required for all quantum mechanics students
Review: Even after taking 3 semesters of quantum mechanics, I felt like I had a pretty shaky grasp on topics such as selection rules and the addition of angular momenta. I had heard about the important role that group theory plays in quantum mechanics, so I took a mathematics class in abstract algebra. Though this covered a lot of interesting topics in group structure and ring theory, I was left with almost no idea how the material applied to quantum mechanics. Tinkham's book is invaluable in that it develops the parts of group theory that are extremely relevant to physics and chemistry such as the theory of representations (topics that mathematicians seem bored by) and then shows beautifully how it applies to quantum mechanics. Not only did I understand the selection rules, angular momentum, etc... I had a much better understanding of quantum mechanics overall. Group theory makes much more evident what is meant by "good quantum numbers", where degeneracies come from, and other basic issues in quantum mechanics. Particularly clever was the discussion of the Bloch wavefunction ansatz as a consequence of the Abelian symmetry group of a periodic crystal lattice. Invaluable for quantum chemistry, a subject which is touched on, but which was not nearly as developed when the book was written as it is today. Tinkham knows his math, but he knows his physics even better. If you have any interest in quantum mechanics, get this book!