UNIFIED DESCRIPTION OF QUANTUM PARTICLES AND ELECTROMAGNETIC AND ELASTIC-WAVES IN MULTILAYERS

Some relevant mathematical properties of quantum particles, polarized electromagnetic waves and elastic shear horizontal waves in multilayer systems are discussed in a unified way. The time-independent wave equ ations describing these problems are isomorphic for the three cases, b ut the matching boundary conditions are different. These are also desc ribed in common mathematical form by means of appropriate quantities. Phenomenological concepts and parameters of quantum scattering theory are thus related to different transfer matrices often used for both qu antum and classical systems. All multilayers are shown to have the sam e statistical properties beyond characteristic lengths established by an application of the central limit theorem to the different problems. A Poincare map representation which often has practical advantages fo r numerical computation is also set up in a mathematical form common t o all cases.