Nonreflecting Boundary Condition for the Free Schrödinger Equation in 2D

For the numerical solution of wave equations formulated on unbounded domains, one has to restrict the computational domain to a bounded one. It is well-known that imposing any arbitrary boundary condition at the fictitious boundary leads to unphysical reflections. Further, in problems where exact Dirichlet-to-Neumann maps are available, their numerical implementation poses a serious challenge. This work addresses the numerical implementation of one such nonreflecting boundary operator of the form for the free Schrodinger equation on a rectangular computational domain with periodic boundary condition along one of the unbounded directions.