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 is very important to know the basics concepts of group theory, but there is no need to have a deep knowledge as well as to know how to proof all the main theorems. As an introductory course for undergrad students this book is well recommended.

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

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!

A LOT of quantum theory results from symmetry. This book encapsulates a huge amount of results that come directly from group theory. Heavy on actual applied examples. Extremely close to chemistry use, but good for physicists too.

I began reading this book having just finished a course on Abstract Algebra through my school's math department, and the semester before I took a graduate course on the exact subject. 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.

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

BVery good book to read for group theory