Splitting for the semiclassical Schroedinger equation (Christian Lubich, University of Tuebingen)

08.03.2022 11:00

The semiclassically scaled Schroedinger equation describes for example the dynamics of nuclei in molecules. It is computationally challenging because one needs to cope with the double challenge of high dimensions and high oscillations in space and time. This talk is concerned with the time discretization by splitting methods such as the Strang splitting. We review the L^2 error bound, which is quadratic in the stepsize but inversely proportional to the small semiclassical parameter. As a new result, we present and prove an error bound for expectation values of observables, which is of second order uniformly in the semiclassical parameter. The proof uses the known error bound of the Stoermer-Verlet method for the corresponding classical equations of motion in combination with semiclassical analysis.
The talk is based on joint work with Caroline Lasser.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire d'analyse numérique

entrée libre