This book provides an introduction to quantum theory, primarily for mathematics students. It assumes a knowledge of basic algebra and elementary group theory, with little or no familiarity with more advanced topics. Although it takes a traditional approach, the book exploits ideas of linear algebra and points out some of the mathematical subtleties of the theory. It also covers such topics as Bell's inequalities and coherent and squeezed states, and introduces group representation theory, algebraic quantum theory, and quantum statistical mechanics. Later chapters discuss relativistic wave equations and elementary particle symmetries from a group-theoretical standpoint.

• Preface


• Introduction


• Wave mechanics


• Quadratic and linear potentials


• The hydrogen atom


• Scattering and tunnelling


• The mathematical structure of quantum theory


• The commutation relations


• Angular momentum


• Symmetry in quantum theory


• Measurements and paradoxes


• Alternative formulations of quantum theory


• Stationary perturbation theory


• Iterative perturbation theory


• Variational methods


• The semi-classical approximation


• Systems of several particles


• Relativistic wave equation


• Dirac particles in electromagnetic fields


• Symmetries of elementary particles


• A review of linear algebra and groups


• Open systems