Computation of Correlation Functions and Wave Function Projections in the Context of Quantum Trajectory Dynamics
Copyright 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
The following article appeared in
Garashchuk, S. (2007). Computation of correlation functions and wave function projections in the context of quantum trajectory dynamics. The Journal of Chemical Physics, 126, 154104. http://dx.doi.org/10.1063/1.2717931
and may be found at
http://scitation.aip.org/content/aip/journal/jcp/126/15/10.1063/1.2717931
Abstract
The de Broglie-Bohm formulation of the Schrödinger equation implies conservation of the wave functionprobability density associated with each quantum trajectory in closed systems. This conservation property greatly simplifies numerical implementations of the quantum trajectory dynamics and increases its accuracy. The reconstruction of a wave function, however, becomes expensive or inaccurate as it requires fitting or interpolation procedures. In this paper we present a method of computing wave packet correlation functions and wave function projections, which typically contain all the desired information about dynamics, without the full knowledge of the wave function by making quadratic expansions of the wave function phase and amplitude near each trajectory similar to expansions used in semiclassical methods. Computation of the quantities of interest in this procedure is linear with respect to the number of trajectories. The introduced approximations are consistent with approximate quantum potential dynamics method. The projection technique is applied to model chemical systems and to the H+H2exchange reaction in three dimensions.