Journal of Chemical Physics, Vol.117, No.23, 10474-10477, 2002
On quantum trajectories and an uncertainty relation
We discuss quantum trajectories from the point of view of Bohm and Wyatt. We find that the theory can be formally written in terms of a field (probability) [P(x,t)], a position [x], and an average momentum [ ] in a density operator which is normalized and Hermitian, but not positive definite. One consequence of this is that the theory obeys, in a natural way, a formal relation DeltaxDeltap=0 for these averages. We interpret this as a consistency requirement for a trajectory in space-time with a position x and an average momentum which allows a space-time description. We show that a momentum space form can be written in terms of a field (probability) [P(p,t)], a momentum [p], and an average position []. We briefly discuss potential chemical applications of quantum trajectories in the theory of chemical dynamics, kinetics, and local field theory.