Applied Group Theory - 1st Edition - ISBN: 9780082031901, 9781483149387

Applied Group Theory

1st Edition

Selected Readings in Physics

Authors: Arthur P. Cracknell
Editors: D. ter Haar
eBook ISBN: 9781483149387
Imprint: Pergamon
Published Date: 1st January 1968
Page Count: 430
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Selected Readings in Physics: Applied Group Theory provides information pertinent to the fundamental aspects of applied group theory. This book discusses the properties of symmetry of a system in quantum mechanics.

Organized into two parts encompassing nine chapters, this book begins with an overview of the problem of elastic vibrations of a symmetric structure. This text then examines the numbers, degeneracies, and symmetries of the normal modes of vibration. Other chapters consider the conditions under which a polyatomic molecule can have a stable equilibrium configuration when its electronic state has orbital degeneracy. This book discusses as well the effect of an electric field having a given symmetry upon an atom. The final chapter deals with the symmetry of crystals with a magnetic moment.

This book is intended to be suitable for final-year students and fresh postgraduate students in physics. Physicists and researcher workers will also find this book extremely useful.

Table of Contents


Part 1

I. Symmetry

1.1. Symmetry Operations

1.2. Definition of a Group

1.3. Symmetry in Nature

II. Theory of Groups

2.1. Further Definitions

2.2. Subgroups

2.3. Classes

2.4. Matrices

2.5. Matrices and the Symmetry Operations of the Square

2.6. Matrix Representations of a Group

2.7. Irreducible (Matrix) Representations of a Group

2.8. The Deduction of the Irreducible Representations of a Group

2.9. The Direct Product of Two Groups

2.10. Group Theory and Quantum Mechanics, Wigner's Theorem

III. Crystallographic Groups

3.1. Point Groups

3.2. The Derivation of the Point Groups and their Character Tables

3.3. The Basis of a Representation

3.4. Bravais Lattices

3.5. Space Groups

3.6. Seitz Space-group Symbols

IV. The Rotation, Symmetric and Lorentz Groups

4.1. The Rotation Group

4.2. The Representations of the Rotation Group

4.3. The Spherical Harmonics and the Rotation Group

4.4. The Permutation Group, or Symmetric Group, S(n)

4.5. Young's Tableaux

4.6. Special Relativity and the Lorentz Group

V. Vibrations in Molecules and Solids

5.1. Vibrations of Molecules, Normal Modes

5.2. Example, the Normal Modes of the Methane Molecule

5.3. Vibrations of Solids, Phonons

5.4. Brillouin Zone Theory

5.5. Infra-red and Raman Activity of the Normal Modes

VI. Electronic States in Atoms, Molecules and Solids


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© Pergamon 1968
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About the Author

Arthur P. Cracknell

About the Editor

D. ter Haar

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