Implementation of transparent boundaries for numerical solution of the Schrödinger equation

Abstract This paper deals with the application of the parabolic (Schrodinger) equation to the numerical solution of two-dimensional diffraction problems. Our purpose is to reduce the initial value problem for the halfplane to the boundary value problem for a properly chosen semistrip of finite width. The exact transparency boundary condition has been obtained that transfers the radiation condition posed at infinity to the boundaries of the semistrip. The numerical implementation of the proposed approach in terms of finite differences is described. Several numerical examples are given.