Matrix treatment of wave propagation in stratified media

An analytic approximation for the diffeomorphism of a homogeneous linear second-order differential equation is obtained in matrix representation. As a consequence of energy conservation for waves propagating in a non-absorbing stratified medium the corresponding transmission matrix belongs to the group QU(2). The approximation contains the WKB approximation and may be applied to discrete and continuous media. As an application of the method three specific problems are treated: calculation of the reflection coefficient, determination of the eigenmodes, and calculation of the adiabatic invariant for a damped classical harmonic oscillator.