Solution of the time-dependent, multi-particle Schrödinger equation using Monte Carlo and numerical integration

We study the solution of the multi-particle, time-dependent Schrödinger equation using quantum Monte Carlo methods and numerical integration. The Monte Carlo method is based on a mixed scheme, combining classical dynamics for the nuclei and quantum mechanics for the electrons. The numerical solution uses a discretization of the Schrödinger equation in real space and time. The two methods have been applied to light elements and silicon, respectively, and the dynamical events considered are the dissociation of H 3 and the fragmentation of small silicon clusters. Benchmark calculations, performed for the ground state of H, He and small clusters of H and Si, are compared with Hartree–Fock calculations, also carried out in the course of this study. This comparison shows that both methods regain the exact stationary limit.