This book covers one of the most efficient approximation methods for the theoretical analysis and solution of problems in theoretical physics and applied mathematics. The method can be applied to any field involving second order ordinary differential equations. It is written with practical needs in mind, with 50 solved problems covering a broad range of subjects and making clear which concepts and results of the general theory are needed in each case.

The result of two decades spent developing and refining the phase-integral method to a high level of precision, the authors have applied this method to problems in various fields of theoretical physics. The problems treated are of a mathematical nature, but have important physical applications. This book will thus be of great use to research workers in various branches of theoretical physics, where the problems can be reduced to one-dimensional second-order differential equations of the Schrodinger type for which phase-integral solutions are required. Includes contributions from notable scientists who have already made use of the authors'technique."

This book provides a thorough introduction to one of the most efficient approximation methods for the analysis and solution of problems in theoretical physics and applied mathematics. It is written with practical needs in mind and contains a discussion of 50 problems with solutions, of varying degrees of difficulty. The problems are taken from quantum mechanics, but the method has important applications in any field of science involving second order ordinary differential equations. The power of the asymptotic solution of second order differential equations is demonstrated, and in each case the authors clearly indicate which concepts and results of the general theory are needed to solve a particular problem. This book will be ideal as a manual for users of the phase-integral method, as well as a valuable reference text for experienced research workers and graduate students.