This edition differs from the second chiefly in the addition of about 100 pages devoted to the quantum (or geometric, or Berry) phase, a subject that did not exist when this book was written. The changes in the remainder of the book consist of corrections of a small number of misprints. While it may seem that adding two chapters on the quantum phase is overemphasizing a currently fashionable subject, they actually complete the development of quantum theory as given in this book. We start with simple models, synthesizing them into complicated "molecules." With the new chap­ ters. we end with complicated "molecules," dividing them into simpler parts. This process of dividing a complex system into parts quite naturally gives rise to a gauge theory, of which the geometric phase is a manifestation - with consequences not only in theory, but observable in experiments. For this rea­ son, the geometric phase is not a mere fashion, but a discovery that will retain its importance forever and must be discussed in textbooks on quantum mechanics. to acknowledge help and advice from Mark Loewe with the I would like writing and also of the new part of the book. In addition, I would like to express my gratitude to J. Anandan, M. Berry, and c.A. Mead, who have read parts or all of the new material and have provided valuable advice.

I Mathematical Preliminaries.- II Foundations of Quantum Mechanics-The Harmonic Oscillator.- III Energy Spectra of Some Molecules.- IV Complete Systems of Commuting Observables.- V Addition of Angular Momenta-The Wigner-Eckart Theorem.- VI Hydrogen Atom-The Quantum-Mechanical Kepler Problem.- VII Alkali Atoms and the Schrödinger Equation of One-Electron Atoms.- VIII Perturbation Theory.- IX Electron Spin.- X Indistinguishable Particles.- XI Two-Electron Systems-The Helium Atom.- XII Time Evolution.- XIII Some Fundamental Properties of Quantum Mechanics.- XIV Transitions in Quantum Physical Systems-Cross Section.- XV Formal Scattering Theory and Other Theoretical Considerations.- XVI Elastic and Inelastic Scattering for Spherically Symmetric Interactions.- XVII Free and Exact Radial Wave Functions.- XVIII Resonance Phenomena.- XIX Time Reversal.- XX Resonances in Multichannel Systems.- XXI The Decay of Unstable Physical Systems.- XXII Quantal Phase Factors and Their Consequences.- XXIIIA Quantum Physical System in a Quantum Environment-The Gauge Theory of Molecular Physics.- Epilogue.