Gauss-Hermite wavepacket dynamics: convergence of the spectral and pseudo-spectral approximation
Résumé
The time dependent linear Schrödinger equation for nuclei on the whole space is semi-discretised using Hermite and Gauss-Hermite basis functions. These are well suited on the one hand for the conservation properties of the numerical solution and, on the other hand, for their remarkable approximation properties. We investigate theoretically and numerically the convergence of the spectral and pseudo- spectral Gauss-Hermite semi-discretisation schemes. Schrödinger equation, Gauss- Hermite approximation, spectral and pseudo-spectral methods