The approximate use of the complex gamma function in some wave propagation problems

Abstract

After a historical survey of the problem of the potential barrier, and an examination of the types of approximations, introduced and the reason for them, certain fallacious processes are discussed whereby the complex gamma function is given false approximate representations by means of exponential functions. Two kinds of problems involving complex barriers are then examined; firstly the phenomenon of resonant tunnelling through two complex potential barriers, and secondly, reflection phenomena arising from a single complex barrier The common fallacies are also examined, and the proper treatment of these problems shows when the complex gamma function must be retained and when it can be dispensed with.