A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions

In this paper, we propose a numerical scheme to solve the two-dimensional (2D) time-dependent Schrödinger equation using collocation points and approximating the solution using multiquadrics (MQ) and the Thin Plate Splines (TPS) Radial Basis Function (RBF). The scheme works in a similar fashion as finite-difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme.