Construction and analysis of discretization schemes for one-dimensional nonlocal Schrödinger equations with exact absorbing boundary conditions

The construction of exact absorbing boundary conditions (ABCs) for the one-dimensional nonlocal fully-discrete Schrodinger equation is proposed. The computation of the Green's functions for the discrete nonlocal Schrodinger equation is stated and used to build the ABCs. Numerical error estimates are then proved for the case of a singular interaction kernel. The theory and numerical analysis is supported by numerical examples.