# Classical and Quantum Integrability

Sep 2 – 6, 2019
Institut de Mathématiques de Bourgogne
Europe/Paris timezone

## A hybrid WKB-based method for Schrödinger scattering problems in the semi-classical limit

Sep 3, 2019, 11:45 AM
45m
Amphi Gevrey

### Speaker

Anton Arnold (Vienna University of Technology)

### Description

We consider 1D scattering problems related to quantum transport in diodes. We discuss the efficient numerical integration of ODEs like $\epsilon^2*u"+a(x)*u=0$ for $0<\epsilon<<1$ on coarse grids, but still yielding accurate solutions; including oscillatory (for given $a(x)>0$) and evanescent regimes (for $a(x)<0$), partly including turning points. In the oscillatory case we use a marching method that is based on an analytic WKB-preprocessing of the equation. And in the evanescent case we use a FEM with WKB-ansatz functions.

(co-authors: Claudia Negulescu; Kirian Döpfner; Christian Klein, Bernhard Ujvari)

### Primary author

Anton Arnold (Vienna University of Technology)