progress along these lines has been achieved by the multi-configurational time-dependent Hartree (MCTDH) method, developed by Meyer, Manthe and co-workers.[@meyer90; @manthe92] More recently, time-evolving grid, or “quantum trajectory” methods[@lopreore99; @mayor99; @wyatt99; @wyatt01b; @wyatt01c; @wyatt] (QTMs) have also been developed, and for certain types of systems, successfully applied at quite high dimensionalities.[@wyatt01c; @wyatt]

QTMs are based on the hydrodynamical picture of quantum mechanics, developed over half a century ago by Bohm[@bohm52a; @bohm52b] and Takabayasi,[@takabayasi54] who built on the earlier work of Madelung[@madelung26] and van Vleck.[@vanvleck28] QTMs are inherently appealing for a number of reasons. First, they offer an intuitive, classical-like understanding of the underlying dynamics, which is difficult-to-impossible to extract from more traditional fixed grid/basis methods. In effect, quantum trajectories are like ordinary classical trajectories, except that they evolve under a modified potential $V+Q$, where $Q$ is the wavefunction-dependent “quantum potential” correction. Second, QTMs hold the promise of delivering exact quantum mechanical results without exponential scaling in computational effort. Third, they provide a pedagogical understanding of entirely quantum mechanical effects such as tunneling[@lopreore99; @wyatt] and interference.[@poirier04bohmI; @zhao03] They have already been used to solve a variety of different types of problems, including barrier transmission,[@lopreore99] non-adiabatic dynamics,[@wyatt01] and mode relaxation.[@bittner02b] Several intriguing 