Exact and approximate methods for the investigation of the propagation of waves through a system of barriers

Abstract

AbstractThere is developed the theory of the propagation of waves through a system of potential barriers. Many properties are derived and discussed, mainly by the use of matrix theory arising from the description of each barrier by a transmission matrix. The extent to which certain previously used approximate methods are applicable and valid is also examined. Two distinct kinds of resonant phenomena are discussed – first when there is no incident wave and secondly when there is no reflected wave. This latter case of perfect transmission is investigated in detail, an examination being given of both why and when it occurs and the time taken to establish such exceptional fields within the barriers.