This graduate-level text develops aspects of group theory most relevant to physics and chemistry and illustrates their applications to quantum mechanics: abstract group theory, theory of group representations, physical applications of group theory, full rotation group and angular momentum, quantum mechanics of atoms, molecular quantum mechanics, and solid-state theory. 1964 edition.

CUSTOMER REVIEWS (Average Customer Rating: 4.5 based on 6 reviews)

Heavy on the Math . . .

This book is an excellent reference for group theory. It gives you the detailed math behind group theory (which is great for me). It also gives you a brief introduction so you can work with molecular group theory. This was the recommended text in my chemical group theory class. It serves as a good mathematical reference. Also, see Cotton's group theory book, and Carters group theory book.
September 10, 2007

Good for the Undergrad Students.

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.
August 27, 2007

Most accessible of the useful physics texts

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!
August 10, 2006

A must for every grad student

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.
December 26, 2005

Group Theory and Quantum Mechanics

Both the content of the book and service of amazon are wonderful
July 19, 2005

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Introduction to Superconductivity: Second Edition (Dover Books on Physics)
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Lie Groups for Pedestrians
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Quantum Mechanics in Simple Matrix Form
by Thomas F. Jordan