Phase-integral method

This book is the result of two decades spent by the authors developing and refining the phase-integral method to a high level of precision. The efficiency of the phase-integral method has been shown both analytically and numerically. With the inclusion of supplementary quantities closely related to new Stokes constants and obtained with the aid of comparison equation techniques, important classes of problems in which transition points may approach each other become accessible to accurate analytical treatment. The treatment of material is mathematically rigorous but it has important physical applications that are found in the adjoined papers. This book will be useful to researchers in 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.