Group Theory and Quantum Mechanics - Dover Books on Chemistry | Advanced Physics Textbook for Students & Researchers | Quantum Physics Study & Research Reference

I have attempted to read other books on group theory, especially those intended for physicists, including Weyl's book The Theory of Groups and Quantum Mechanics. Tinkham's book, however, is the only one that I have been able to understand relatively well. Tinkham gently takes you by the hand and starts you out on a tutorial that addresses the symmetry of a simple example from plane geometry, and then gradually builds up to more sophisticated problems. Character tables and the various orthogonality and normalization relations that make them useful are developed and used for both simple (e.g. plane geometry) and more sophisticated problems. Lie Groups, Schur's Lemma, angular momentum, crystal symmetry, and nature's inability to conserve parity are among the topics addressed.The treatment of Lorentz and Poincare groups required for a more sophisticated understanding of quantum field theory, however, is not included in this book--for those topics Weinberg's (The Quantum Theory of Fields, Volume 1: Foundations) suggestion of Tung's Group Theory in Physics would seem to be reasonable. I was also not able to understand Tinkham's proof of the Vector Addition Theorem for angular momentum. I found a version of the proof that I could understand, however, in Wigner's book Group Theory and It's Application to the Quantum Mechanics of Atomic Spectra, and I display this proof along with my review of Wigner's book.