ON THE NUMERICAL SOLUTION OF ONE DIMENSIONAL SCHRODINGER EQUATION WITH BOUNDARY CONDITIONS INVOLVING FRACTIONAL DIFFERENTIAL OPERATORS

In this paper we study of collocation method with Radial Basis Function to solve one dimensional time dependent Schrodinger equation in an unbounded domain. To this end, we introduce artificial boundaries and reduce the original problem to an initial boundary value problem in a bounded domain withtransparent boundary conditions that involves half order fractional derivative in t. Then in three stages we use the Laplace Transform method, the collocation method and finally the Legender expansion method. Numerical examples are given to show the effectiveness of the scheme.

Keywords:

The Schrodinger equation , Collocation method , Radial Basis Function , Fractional derivative boundary condition , Legendre expansion method