Group theory used to improve the efficiency of transfer-matrix computations

Transfer-matrix methodology is frequently used to deal with elastic scatter ing problems that require a solution of Schrodinger or homogeneous Maxwell equations in the continuous part of their spectra. As predicted by group th eory, the basic states used for the expansion of the solutions can be separ ated into independent sets, thus enabling the scattering problem to be solv ed with a drastically improved efficiency. Depending on the peculiar symmet ry in the problem, the basic states can present pairs of "conjugate sets," whose associated characters are complex conjugate of each other. When the p otential energy takes strict real values, the transfer matrices correspondi ng to these conjugate sets have well-defined relationships that enable the transfer matrices of both conjugate sets to be computed from a single propa gation step. This results in a further reduction of up to 50% of the total computation time. This paper presents the way group theory can be used syst ematically to improve the efficiency of transfer-matrix computations. In a first part, the basic states are separated into independent sets. Relations hips between the transfer matrices corresponding to conjugate sets are then derived. The theory is finally illustrated by a simulation of electronic s cattering by a C-60 molecule in a projection configuration. [S1063-651X(99) 06912-3].