... for all readers interested in specific aspects of perturbation methods, path integrals, and their applications in classical field theory, this book provides a valuable source for their studies. -- Mathematical Reviews
It will be useful for theoretical physicists who wish to enlarge their skill in quantum mechanics and for postgraduate students studying quantum mechanics on a deep level.
After a consideration of basic quantum mechanics, this introduction aims at a side by side treatment of fundamental applications of the Schrödinger equation on the one hand and the applications of the path integral on the other. Different from traditional texts and using a systematic perturbation method, the solution of Schrödinger equations includes also those with anharmonic oscillator potentials, periodic potentials, screened Coulomb potentials and a typical singular potential, as well as the investigation of the large order behavior of the perturbation series. On the path integral side, after introduction of the basic ideas, the expansion around classical configurations in Euclidean time, such as instantons, is considered, and the method is applied in particular to anharmonic oscillator and periodic potentials. Numerous other aspects are treated on the way, thus providing the reader an instructive overview over diverse quantum mechanical phenomena, e.g. many! other potentials, Green’s functions, comparison with WKB, calculation of lifetimes and sojourn times, derivation of generating functions, the Coulomb problem in various coordinates, etc. All calculations are given in detail, so that the reader can follow every step.