Short Time Quantum Propagator and Bohmian Trajectories

Abstract

We begin by giving correct expressions for the short-time action; following the work of one of us and Makri--Miller. We use these estimates to derive a correct expression modulo modulo delta(t)sqr for the quantum propagator and we show that the quantum potential is negligible modulo delta(t)sqr for a point source. We finally prove that this implies that the quantum motion is classical for very short times.