Introduction to Group Theory with Applications

Materials Science and Technology

Gerald Burns, Allen M. Alper, A. S. Nowick

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780121457501
• eBook ISBN:
  9781483191492
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Introduction to Group Theory with Applications covers the basic principles, concepts, mathematical proofs, and applications of group theory. This book is divided into 13 chapters and begins with discussions of the elementary topics related to the subject, including symmetry operations and group concepts. The succeeding chapters deal with the properties of matrix representations of finite groups, the vibrations of molecular and crystals, vibrational wave function, selection rules, and molecular approximations. These topics are followed by reviews of the basic of quantum mechanics, crystal field theory, atomic physics, hybrid functions, and molecular orbital theory. The last chapters describe the symmetry of crystal lattices, the band theory of solids, and the full rotation group. This book will be of value to undergraduate mathematics and physics students.

Table of contents

• Front Cover
• Introduction to Group Theory with Applications
• Copyright Page
• Table of Contents
• Dedication
• PREFACE
• ACKNOWLEDGMENTS
• Chapter 1. SYMMETRY OPERATIONS
• Chapter 2. GROUP CONCEPTS
• Chapter 3. MATRIX REPRESENTATIONS OF FINITE GROUPS
• Chapter 4. CHARACTERS OF MATRIX REPRESENTATIONS OF FINITE GROUPS
• Chapter 5. VIBRATIONS OF MOLECULES AND CRYSTALS
• Chapter 6. NORMAL MODES (DIRECT PRODUCT AND SELECTION RULES)
• Chapter 7. QUANTUM MECHANICS
• Chapter 8. CRYSTAL FIELD THEORY (AND ATOMIC PHYSICS)
• Chapter 9. HYBRID FUNCTIONS
• Chapter 10. MOLECULAR ORBITAL THEORY
• Chapter 11. SYMMETRY OF CRYSTAL LATTICES
• Chapter 12. BAND THEORY OF SOLIDS
• Chapter 13. THE FULL ROTATION GROUP
• Appendix 1: CRYSTAL SYSTEMS
• Appendix 2: THE 32 POINT GROUPS
• Appendix 3: CHARACTER TABLES
• Appendix 4: SPACE GROUPS
• Appendix 5: MATRICES, VECTOR SPACES, AND LINEAR OPERATORS
• Appendix 6: DIRECT PRODUCT TABLES
• Appendix 7: CORRELATION TABLES
• Appendix 8: SPHERICAL HARMONICS
• Appendix 9: TANABE–SUGANO DIAGRAMS
• Appendix 10: DOUBLE GROUP CHARACTER TABLES
• BIBLIOGRAPHY
• INDEX