High Order Scheme for Schrödinger Equation with Discontinuous Potential I: Immersed Interface Method

Abstract

The immersed interface method is modified to compute Schrödinger equation with discontinuous potential. By building the jump conditions of the solution into the finite difference approximation near the interface, this method can give at least second order convergence rate for the numerical solution on uniform cartesian grids. The accuracy of this algorithm is tested via several numerical examples.