Trajectory driven second quantization approach to quantum dynamics

We present a second quantization formulation of quantum dynamics and investigate the new formulation by solving the time-dependent Schroedinger equation for a three dimensional quantum system in two ways. Firstly by introducing a state expansion of the wave function in a Gauss-Hermite basis set and secondly by using the second quantization scheme derived by expanding the potential locally around trajectories. The system under investigation is that of a helium atom scattered from a copper surface. The complete system can by introducing a time-dependent Hartree approximation be reduced to that of solving a time-dependent Schroedinger equation for the motion of the helium atom in an effective time-dependent potential. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)