Transfer-matrix methodology with stability-control techniques

The transfer-matrix methodology is frequently used to deal with elastic scattering problems that require a solution of the Schrödinger or homogeneous Maxwell equations in the continuous part of their spectra. In its basic formulation, this technique however reveals limited by numerical instabilities, which can be drastically reduced by application of the layer addition algorithm. By providing each transfer matrix with an accuracy estimator, it possible to predict and monitor the precision of the computation as a function of the number of layers, thus enabling a quantitative control of the stability. Beside this control of stability, other recent progress were achieved in the transfer-matrix methodology, i.e. improvements due to group theory, consideration of non-square matrices, combination with the Green-function formalism. This paper is essentially an overview of these various extensions of the method, which are illustrated by simulations of electronic scattering by a C60 molecule in a projection configuration. Key-Words: electronic scattering, non-square transfer matrix, numerical stability, Green functions, group theory