Jan 16 – 20, 2023
Europe/Paris timezone

Anton Arnold: "A hybrid WKB-based method for Schrödinger scattering problems in the semi-classical limit"

Jan 17, 2023, 9:00 AM
Amphithéâtre Schwartz (IMT)

Amphithéâtre Schwartz


Université Paul Sabatier, 118 Route de Narbonne, 31000 Toulouse France


We consider 1D scattering problems related to quantum transport in diodes. We discuss the efficient numerical integration of ODEs like epsilon^2u"+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. Then we shall discuss two approaches to couple the oscillatory regime to smooth regimes across turning points and close to them: In the former (evanescent) case we use a FEM with WKB-ansatz functions; in the latter case an automated switching to a Runge-Kutta method with adaptive step size controller.

Co-authors: Claudia Negulescu; Kirian Döpfner, Jannis Körner; Christian Klein, Bernhard Ujvari

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