Mathematical concepts of open quantum boundary conditions

Abstract

This paper is concerned with the derivation and the numerical discretization of open boundary conditions for the 1D Schrödinger equation in order to simulate quantum devices. New discrete transparent boundary conditions are presented that are able to handle the situation of a continuous plane wave influx into a device. Also, we give a review of various formulations of boundary conditions that are used within the Schrödinger and the Wigner formalism of quantum mechanics, and we discuss their mathematical properties.