### Abstract

This talk, which is based on joint work with Erwan Faou and Vasile Gradinaru, reports on work in progress on a newly developed numerical approach to many-body quantum dynamics in the semi-classical regime. We present a symmetric splitting integrator for the propagation of multidimensional extensions of Gauss-Hermite wavepackets appearing in analytical work by Hagedorn. The integrator evolves positions and momenta of the wavepackets according to the Stoermer-Verlet integrator of classical mechanics, and gains its computational feasibility and efficiency for many particles by the possibility of thinning out the moving basis sets according to a hyperbolic cross approximation or a Hartree-type approximation in a moving frame. The algorithm reduces to the Strang splitting of the Schroedinger equation in the limit of the full set of orthonormal basis functions, and it is robust in the semiclassical limit.