On the Numerical Solution of One Dimensional Schrodinger Equation with Boundary Conditions Involving Fractional Differential Operators

In this paper we study ofcollocation 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 with transparent boundary conditions that involves halforder 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 ofthe scheme.