Moreover, since the "quantum potential" (whose gradient is the negative quantum force) has an inverse dependence on density, the numerical derivatives become unstable in the vicinity of wavefunction nodes, leading to a breakdown of the simulation-the so-called "node problem." Various treatments for these numerical issues have been proposed in the literature-e.g., the moving least squares (MLS) approach, finite differences for constrained trajectories in an arbitrary Lagrangian-Eulerian (ALE) moving frame, 20 artificial viscosity forces, "bipolar" decompositions of the wavefunction, and semiclassical treatments based on linearized quantum forces. More recently, a fundamentally different QTM-type approach has been developed, based on a complete reformulation of quantum theory in terms of trajectories. In this approach one still works with the same ensemble of quantum trajectories as in the original Bohmian QTM formulation described above. However, instead of using those trajectories to propagate the wavefunction-based hydrodynamic fields, the quantum force is computed directly from the trajectories themselves-without making any reference to the wavefunction itself. That this is even possible is no trivial development. In any event, from a numerical standpoint, the spatial variable x is replaced with a "trajectory-labelling coordinate" (usually denoted C), in terms of which the numerical grid becomes structured and stationary. This, in turn, leads to enormous numerical advantages in terms of evaluating the derivatives needed to compute the quantum force. Indeed, the trajectory-based form of the quantum force is generally found to overcome the node problem, although in the time-dependent case under-sampling of trajectories in areas of low density impacts the accuracy of finite differences schemes. This is discussed in more details below.