Group Theory and Quantum Mechanics

by Michael Tinkham

This graduate-level text develops the aspects of group theory most relevant to physics and chemistry (such as the theory of representations) and illustrates their applications to quantum mechanics. The first five chapters focus chiefly on the introduction of methods, illustrated by physical examples, and the final three chapters offer a systematic treatment of the quantum theory of atoms, molecules, and solids.
The formal theory of finite groups and their representation is developed in Chapters 1 through 4 and illustrated by examples from the crystallographic point groups basic to solid-state and molecular theory. Chapter 5 is devoted to the theory of systems with full rotational symmetry, Chapter 6 to the systematic presentation of atomic structure, and Chapter 7 to molecular quantum mechanics. Chapter 8, which deals with solid-state physics, treats electronic energy band theory and magnetic crystal symmetry. A compact and worthwhile compilation of the scattered material on standard methods, this volume presumes a basic understanding of quantum theory.

Genres: Physics, Mathematics, Chemistry, Science, Textbooks, Nonfiction

340 pages, Paperback

First published June 1, 1964

Reviews

[Michael Weaver · Rating 4 out of 5]

This book is a great read in that Tinkham develops the parts of group theory which are relevant to physics and chemistry and sufficiently shows how it applies to QM as a whole. Particularly insightful was Tinkhams discussions of the Bloch wavefunction as a consequence of the Abelian symmetry group. Although overall I was pleased and would recommend it, I did find a few of things that were lagging. Some of the views are a little outdated specifically the applications to molecular QM, particularly in leiu of Ligand-Field Theory and he doesn't really cover the effects of antisymmetric wavefunctions for electrons nor ever mentions Mulliken in molecular QM. The rest of the book is engaging as it does not waste time with trivial examples but dives quickly into the language of group theory.

[Kyle · Rating 3 out of 5]

oh, i always wanted to steer clear of group theory. but needing to know a little group theory in part, this book was recommended to me as a place to start.