EFFICIENT SOLUTION OF TIME DEPENDENT SCHRODINGER EQUATION WITH ARTIFICAL BOUNDARY CONDITION

In this paper, we introduce an artificial boundary conditions for the numerical solution of the Schrodinger equation on an infinite domain. We get an initial-boundary value problem with a finite computational domain which is equivalent to the original problem. . Then we propose a polynomial basis set that is extendable to any desired higher-order accuracy. This method is based on the Constrained Interpolation Profile method. The numerical example shows the effectiveness of the scheme.