For particle physicists, mathematical physicists and high-energy physicists, this book introduces modern developments on the bound state problem in Schrödinger potential theory and its applications in particle physics. The Schrödinger equation provides a framework for dealing with energy levels of N-body systems. It was a cornerstone of the quantum revolution in physics of the twenties but reemerged in the eighties as a powerful tool in the study of spectra and decay properties of mesons and baryons. Beginning with a detailed study of two-body problems, including discussion of general properties, level ordering problems, energy level spacing and decay properties, this book treats relativistic generalizations, and the inverse problem. Finally, 3-body problems and N-body problems are dealt with. Considers particle and atomic physics as well as quarkonium spectroscopy. The emphasis throughout is on showing how the theory can be tested by experiment. Many references are provided.