Group Theory and Quantum Mechanics (Dover Books on Chemistry) Paperback – 1 Jan 2004
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About the Author
Tinkham is Rumford Professor of Physics, and Gordon McKay Professor of Applied Physics, Harvard University.
Most Helpful Customer Reviews on Amazon.com (beta)
After taking the math course, I was presented with group theory as if it were some muddled mix of facts, and the course came across as a poorly taught class on number theory. After reading just the first chapter of Tinkham's book, I developed a new, deeper understanding of group theory as a whole. For example, the way that Tinkham presents normal subgroups makes vastly more intuitive sense than the presentation I received in my math course.
The first two chapters alone are probably worth 80% of the book's sale price. The rest is made up entirely of the fact that the book does not piddle around with trivial examples, but genuinely frames quantum mechanics in the language of group theory, and the most important part is that Tinkham does it well.
This book, along with his book on superconductivity, are must-haves for any serious condensed matter person, and this book should be at least read (if not owned) by any physics grad student.
Tinkham's text is the first textbook one should go to for a reasonably rigorous introduction to the theory and use of group representations in physics and theoretical chemistry. Modern theoretical chemists should become familiar with all of this book, with the possible exception of the some of the material in Chapter 5 that will be applicable only to physicists (and not a lot of that, actually). The pervasiveness of band theory, even in general inorganic chemistry journals now, should convince chemists who teach this subject to include a lot of Chapter 8 (Solid-State Theory) and chemical theorists will even have to go beyond the symmorphic groups treated here.
The purely mathematical aspects of the subject are treated briefly, but much more completely, than "chemical group theory books" like Cotton's, for example. Naturally, this comes at a price of more mathematical abstractness, but that is unavoidable. These sections, like the rest of the book, are very well written.
Chapter 7, on applications to molecular quantum mechanics, is now quite dated. It was quite incomplete even when written, since it did not include any discussion of ligand-field theory. The effects of antisymmetric wavefunctions for electrons are touched on briefly in Chapter 5 (atoms), but are not adequately accounted for in discussion of molecules. (Incidentally, the failure to use Mulliken notation in molecular QM is an unfortunate annoyance.)
These objections aside, this book is an excellent buy for the price of a Dover edition. Indeed, if I'd included price in my rating, it would be 5 stars - easily!
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.
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