JWKB approximation: contributions to the theory

The book contains a rigorous treatment of the one-dimensional JWBK-approximation. Using the ideas introduced by Zwaan and Kemble as a starting point we develop a method for examining the properties of the JWKB-approximation which is powerful also in intricate and complicated applications. In the first place we have had quantal problems in mind and hence, in the main part of the book, we assume the coefficients of the differential equation considered to be real on the real axis. This assumption simplifies the treatment. There are, however, important applications, for instance in the theory of electromagnetic waves, where the reality condition is not fulfilled. It should therefore be pointed out that the general theory in chapters 3, 4, and 7, is not subject to the above mentioned restriction and that the method can be worked out also when the coefficients are complex.