An Introduction to Phase-Integral Methods by John Heading
The phase-integral method in mathematics, also known as the Wentzel-Kramers-Brillouin (WKB) method, is the focus of this introductory treatment. Author John Heading successfully steers a course between simplistic and rigorous approaches to provide a concise overview for advanced undergraduates and graduate students in mathematics and physics. Since the number of applications is vast, the text considers only a brief selection of topics and emphasizes the method itself rather than detailed applications. The process, once derived, is shown to be one of essential simplicity that involves merely the application of certain well-defined rules. Starting with a historical survey of the problem and its solutions, subjects include the Stokes phenomenon, one and two transition points, and applications to physical problems. An appendix and bibliography conclude the text.
Preface I Historical Survey of the Problem II The W.K.B.J. Solutions III The Stokes Phenomenon IV One Transition Point V Two Transition Points VI Applications to Physical Problems Appendix: The Relationship Between Series and the W.K.B.J. Solutions Bibliography Index