in time. Several numerical methods, both “exact” and approximate, are currently being developed to deal with this important problem. The latter category includes the artificial viscosity[@kendrick03; @pauler04] and linearized quantum force methods,[@garashchuk04] both of which have proven to be very stable. While such approximate methods may not capture the hydrodynamic fields with complete accuracy in nodal regions, they do allow for continued evolution and long-time solutions, often unattainable via use of a traditional QTM. The “exact” methods include the adaptive hybrid methods,[@hughes03] and the complex amplitude method.[@garashchuk04b] In the adaptive hybrid methods, for which hydrodynamic trajectories are evolved everywhere except for in nodal regions, where the time-dependent Schrodinger equation is solved instead to avoid node problems. Although they have been applied successfully for some problems, these methods are difficult to implement numerically, since not only must the hydrodynamic fields be somehow monitored for forming singularities, but there must also be an accurate means for interfacing and coupling the two completely different equations of motion. The complex amplitude method is cleaner to implement, but is only exact for linear and quadratic Hamiltonians.

In a recent paper,[@poirier04bohmI] hereinafter referred to as “paper I,” one of the authors (Poirier) introduced a new strategy 