An Introduction to Groups and their Matrices for Science Students

Robert Kolenkow

• Publisher: Cambridge University Press
• Year: 2022
• Print ISBN:
  9781108831086
• eBook ISBN:
  9781108912631
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

Group theory, originating from algebraic structures in mathematics, has long been a powerful tool in many areas of physics, chemistry and other applied sciences, but it has seldom been covered in a manner accessible to undergraduates. This book from renowned educator Robert Kolenkow introduces group theory and its applications starting with simple ideas of symmetry, through quantum numbers, and working up to particle physics. It features clear explanations, accompanying problems and exercises, and numerous worked examples from experimental research in the physical sciences. Beginning with key concepts and necessary theorems, topics are introduced systematically including: molecular vibrations and lattice symmetries; matrix mechanics; wave mechanics; rotation and quantum angular momentum; atomic structure; and finally particle physics. This comprehensive primer on group theory is ideal for advanced undergraduate topics courses, reading groups, or self-study, and it will help prepare graduate students for higher-level courses.

Table of contents

• Cover
• Half-title Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• 1 Fundamental Concepts
• 2 Matrix Representations of Discrete Groups
• 3 Molecular Vibrations
• 4 Crystalline Solids
• 5 Bohr's Quantum Theory and Matrix Mechanics
• 6 Wave Mechanics, Measurement, and Entanglement
• 7 Rotation
• 8 Quantum Angular Momentum
• 9 The Structure of Atoms
• 10 Particle Physics
• Appendix A Character Tables from Class Sums
• Appendix B Born–Jordan Proof of the Quantization Condition
• Appendix C Weyl Derivation of the Heisenberg Uncertainty Principle
• Appendix D EPR Thought Experiment
• Appendix E Photon Correlation Experiment
• Appendix F Tables of Some 3-j Coefficients
• Appendix G Proof of the Wigner–Eckart Theorem
• Index