An Introduction to Phase-Integral Methods

An Introduction to Phase-Integral Methods by John Heading provides a concise overview of the phase-integral method in mathematics, also known as the Wentzel-Kramers-Brillouin (WKB) method. This introductory treatment steers a course between simplistic and rigorous approaches, making it accessible to advanced undergraduates and graduate students in mathematics and physics.

The text focuses on the method itself, rather than its numerous applications, which are vast but not exhaustively covered. Instead, the author explores the process of deriving the phase-integral method and shows how it involves applying well-defined rules. A historical survey of the problem and its solutions is also included, along with discussions of the Stokes phenomenon, one and two transition points, and physical problem applications.

The book concludes with an appendix and bibliography, providing further resources for readers who wish to delve deeper into the subject. With its clear and concise approach, An Introduction to Phase-Integral Methods is a valuable resource for anyone looking to understand this important mathematical technique.