Absorbing Boundary Conditions for the Schrödinger Equation

. A large number of differential equation problems which admit traveling waves have very large (typically infinite) naturally defined domains, with boundary conditions defined at the domain boundary. To be able to numerically solve these problems in smaller subdomains of the original domain, artificial boundary conditions must be defined for these subdomains. One type of artifical boundary conditions which can minimize the size of such subdomains are absorbing boundary conditions. The imposition of absorbing boundary conditions is a technique used to reduce the necessary spatial domain when numerically solving partial differential equations that admit traveling waves. Such absorbing boundary conditions have been extensively studied in the context of hyperbolic wave equations. In this paper, general absorbing boundary condition will be developed for the Schrodinger equation with one spatial dimension, using group velocity considerations. Previously published absorbing boundary condition..