One of the key components of modern physics, quantum mechanics is used in such fields as chemistry, electrical engineering, and computer science. Central to quantum mechanics is Schrodinger's Equation, which explains the behavior of atomic particles and the energy levels of a quantum system. Robert Gilmore's innovative approach to Schrodinger's Equation offers new insight into quantum mechanics at an elementary level. Gilmore presents compact transfer matrix methods for solving quantum problems that can easily be implemented on a personal computer. He shows how to use these methods on a large variety of potentials, both simple and periodic. He shows how to compute bound states, scattering states, and energy bands and describes the relation between bound and scattering states. Chapters on alloys, superlattices, quantum engineering, and solar cells indicate the practical application of the methods discussed. Gilmore's concise and elegant treatment will be of interest to students and professors of introductory and intermediate quantum courses, as well as professionals working in electrical engineering and applied mathematics.