After a few initial chapters on the basics of Mathematica
, the logic of this book is controlled by group theory.
The book has three major parts. Part I begins with the most elementary symmetry concepts, showing how to express them in terms of matrices and permutations, before moving on to the construction of mathematical groups. In Part II, mathematical group theory is presented with motivating questions and experiments first, and theorems that answer those questions second. In Part III, the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems, which are now seen to fall within a unified intellectual framework.
Intended for students of chemistry and molecular physics, the book may be read either independently or on a computer screen with Mathematica
running behind it. The included CD-ROM presents the entire content of the book plus interactive examples using Mathematica
notebooks for problem-solving and learning.
Introduction | A Tutorial on Notebooks | A Basic Mathematica
Tutorial | The Meaning of Symmetry | Axioms of Group Theory | Several Kinds of Groups | The Fundamental Theorem | The Multiplication Table | Molecules | The Point Groups | Euler Rotation Matrices | Lie's Axis-Angle Rotations | Recognizing Matrices | Introduction to the Character Table | The Operator MakeGroup
| Product Groups | Naming the Point Groups | Tabulated Representations of Groups | Visualizing Groups | Subgroups | Lagrange's Theorem | Classes | Symmetry and Quantum Mechanics | Transformation of Functions | Matrix Representations of Groups | Similar Representations | The MakeRep
Operators | Reducible Representations | The MakeUnity
Operator | Schur's Reduction | Schur's First Lemma | Schur's Second Lemma | The Great Orthogonality | Character Orthogonalities | Reducible Rep Analysis | The Regular Representation | Projection Operators | Tabulated Bases for Representations | Quantum Matrix Elements | Constructing SALCs | Hybrid Orbitals | Vibration Analysis | Multiple Symmetries | One-Photon Selection Rules | Two-Photon Tensor Projections | Three-Photon Tensor Projections | Class Sums and Their Products | Make a Character Table | Appendices
, Tutorial and Reference