NUMERICAL STUDIES ON TWO-DIMENSIONAL SCHRODINGER EQUATION BY CHEBYSHEV SPECTRAL COLLOCATION METHOD

A Chebyshev spectral collocation method for computing highly accurate numerical solutions of the two-dimensional Schrodinger equation is proposed. In this method, the equation is first discretized with respect to the spatial variables, transforming the original problem into a set of ordinary differential equations, and then the resulting system of ordinary differential equations are integrated in time by the classical fourth order Runge-Kutta method. Spatial discretization is done by using the Chebyshev spectral collocation method. The comparison between the numerical solution and the exact solution for the test cases shows the good accuracy of the present method.