Scattering Matrix of the One-Dimensional Schrodinger Equation with Arbitrary Potential

This article presents a new highly accurate and efficient method to determine the scattering matrix (SM) of one-dimensional Schrodinger equations with arbitrary potentials. The method allows iterative computation of one SM in terms of the SM of its subsystems, where the SM obtained at each iteration-step do not depend on the properties of their neighbors. This fact makes the SM unitary, avoiding computational instabilities during calculations, and allows high accuracy calculations of SM when potential is given as a series. Finally, the accuracy of the method is tested by using polynomial approximations in a sinusoidal potential and a potential barrier with smooth edges.