Mathematical Models for Transport in Macroscopic and Mesoscopic Systems - Abstract

Arnold, Anton

Numerical WKB-scheme for the stationary Schrödinger equation

We present a new second order finite difference scheme for the Schrödinger equation (scalar and vectorial) in the highly oscillatory regime. Transforming out the dominant oscillations, it is not necessary to resolve each oscillation. Moreover, in the classical limit the scheme reproduces the correct weak limit using just a constant number of grid points.