Resolution of Schrödinger's equation for a scattering problem by a finite‐element method

Abstract

We present a new numerical method for solving the Schrodinger equation in the case of scattering or tunneling states. As an example, we study a model of the scanning tunneling microscope. The method uses a finite-element approximation of the wave function in the region of the scattering potential. From the wave function that we obtain, we derive the tunnel current density. 0 1993