Numerical implementation of absorbing and injecting boundary conditions for the time-dependent Schrödinger equation

Abstract

A method is described that enables the absorption and injection of wave functions at the boundaries of a region in a numerical solution to the time-dependent Schrödinger equation. A number of results corresponding to one- and two-dimensional simulations are presented. Such boundary conditions enable the use of time-dependent simulations of geometries connected to contacts that correspond to sources and sinks of particles in thermal equilibrium. The approach presented has a number of attractive features from a numerical-implementation point of view. © 1995 The American Physical Society.