2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114988The two-by-two scattering matrix for one-dimensional scattering processes is a three-parameter Sp(2) matrix or its unitary equivalent. For one-dimensional crystals, it would be repeated applications of this matrix. The problem is how to calculate N repeated multiplications of this matrix. It is shown that the original Sp(2) matrix can be written as a similarity transformation of Wigner's little group matrix which can be diagonalized. It is then possible to calculate the repeated applications of the original Sp(2) matrix.LaTex 5 pages, presented at 26th International Colloquium on Group Theoretical Methods in Physics (New York, June 2006)Mathematical PhysicsMaterials ScienceQuantum Physicstext