Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential

Xavier Antoine (1, 2) , Christophe Besse (3) , Pauline Klein (2, 3, 1)

1 EDP - Equations aux dérivées partielles
2 CORIDA - Robust control of infinite dimensional systems and applications
3 SIMPAF - SImulations and Modeling for PArticles and Fluids

Mathematical constructions and comparisons of accurate absorbing boundary conditions for the one-dimensional Schrödinger equation with a general variable repulsive potential are developed. Stable semi-discretization schemes are built for the associated initial boundary value problems. Finally, some numerical simulations give a comparison of the various absorbing boundary conditions and show that they yield accurate computations.

Mots clés: Schrödinger equation; Artificial boundary condition; Exterior potential; Unconditionally stable discretization schemes; Numerical simulations

Domaines: Analyse numérique [math.NA]

Xavier Antoine, Christophe Besse, Pauline Klein. Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential. Journal of Computational Physics, 2009, 228 (2), pp.312-335. ⟨10.1016/j.jcp.2008.09.013⟩. ⟨hal-00347888⟩