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 Schrödinger equation is proposed. An efficient computation of the Green's functions for the discrete nonlocal Schrödinger equation is stated and used to build the ABCs. Numerical error estimates are then proved for the case of a singular interaction kernel through a novel way. The theory and numerical analysis is supported by numerical examples.