by Kai S Lam (California State Polytechnic University, USA)

Table of Contents (65k)
Preface (87k)
Chapter 1: How Did Schrödinger Get His Equation? (271k)
Chapter 2: Heisenberg's Matrix Mechanics and Dirac's Re-creation of it (152k)

This textbook is mainly for physics students at the advanced undergraduate and beginning graduate levels, especially those with a theoretical inclination. Its chief purpose is to give a systematic introduction to the main ingredients of the fundamentals of quantum theory, with special emphasis on those aspects of group theory (spacetime and permutational symmetries and group representations) and differential geometry (geometrical phases, topological quantum numbers, and Chern–Simons Theory) that are relevant in modern developments of the subject. It will provide students with an overview of key elements of the theory, as well as a solid preparation in calculational techniques.

• Why is Group Theory Useful in Quantum Mechanics?
• Irreducible Representations of SU(2) and SO(3), Rotation Matrices
• The Symmetric Groups
• The Lie Algebra of SO(4) and the Hydrogen Atom
• Geometric Phases: The Aharonov–Bohm Effect and the Magnetic Monopole
• The Berry Phase in Molecular Dynamics
• The Dynamic Phase: Riemann Surfaces in the Semiclassical Theory of Non-Adiabatic Collisions; Homotopy and Homology
• “The Connection is the Gauge Field and the Curvature is the Force”: Some Differential Geometry
• Topological Quantum (Chern) Numbers: The Integer Quantum Hall Effect
• Chern–Simons Forms: The Fractional Quantum Hall Effect, Anyons and Knots
• and other chapters