  Quantum trajectories, originating from the de Broglie-Bohm (dBB) hydrodynamic
description of quantum mechanics, are used to construct time-correlation
functions in an initial value representation (IVR). The formulation is fully
quantum mechanical and the resulting equations for the correlation functions
are similar in form to their semi-classical analogs but do not require the
computation of the stability or monodromy matrix or conjugate points. We then
move to a {\em local} trajectory description by evolving the cumulants of the
wave function along each individual path. The resulting equations of motion are
an infinite hierarchy, which we truncate at a given order. We show that
time-correlation functions computed using these approximate quantum
trajectories can be used to accurately compute the eigenvalue spectrum for
various potential systems.
