Numerical time-dependent solutions of the Schrödinger equation with piecewise continuous potentials

We consider accurate numerical solutions of the one-dimensional time-dependent Schrödinger equation when the potential is piecewise continuous. Spatial step sizes are defined for each of the regions between the discontinuities and a matching condition at the boundaries of the regions is employed. The Numerov method for spatial integration is particularly appropriate to this approach. By employing Padé approximants for the time-evolution …