Group Theory and Quantum Mechanics (Dover Books on Chemistry)

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.

This book is great. It's opened my eyes to the symmetries that can provide intuition for a lot of the results in quantum mechanics, molecular theory, and solid state physics. I've now become a lot more comfortable with how operators' invariances give rise to their properties. Diagonalization is much more natural of an idea to me now.Prerequisites & Notes: Already be familiar with group theory and quantum mechanics (the latter at the undergraduate level is fine). The first three chapters present a dense overview of group theory and notation that will be used in the rest of the book. I've had two introductions to group theory and that was still barely enough to get me through those chapters. The content was nevertheless interesting, so long as you reread it enough to understand what Tinkham is going on about! (Again, pretty dense)

This book has the advantage of applying group theory directly to solvable physical problems. In most areas of applied physics it isvery important to know the basics concepts of group theory, butthere is no need to have a deep knowledge as well as to know how toproof all the main theorems. As an introductory course for undergradstudents this book is well recommended.

Me agrada mucho para el estudio del acoplamiento espín-órbita.

Great for QM lovers!

Great book great price

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!

My background is that of theoretically inclined inorganic chemist and this review is intended for those with interests in inorganic and physical chemistry or solid-state chemistry/physics.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!

BVery good book to read for group theory

The printing of the book is seriously disappointing. It seems just a horrible copy version. Very low quality! But the content is good.