Artificial boundary conditions for the semi-discretized one-dimensional nonlocal Schrödinger equation

A general method is proposed to build exact artificial boundary conditions for the one-dimensional nonlocal Schrodinger equation. To this end, we first consider the spatial semi-discretization of the nonlocal equation, and then develop an accurate numerical method for computing the Green's function of the semi-discrete nonlocal Schrodinger equation. These Green's functions are next used to build the exact boundary conditions corresponding to the semi-discrete model. Numerical results illustrate the accuracy of the boundary conditions. The methodology can also be applied to other nonlocal models and could be extended to higher dimensions.