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Phase space dynamics in classical mechanics is described by transport alongtrajectories. Anharmonic quantum mechanical systems do not allow for atrajectory-based description of their phase space dynamics. This invalidatessome approaches to quantum phase space studies. We first demonstrate theabsenceof trajectories in general terms. We then give an explicit proof for allquantum phase space distributions with negative values: we show that thegeneration of coherences in anharmonic quantum mechanical systems isresponsible for the occurrence of singularities in their phase space velocityfields, and vice versa. This explains numerical problems repeatedly reported inthe literature, and provides deeper insight into the nature of quantum phasespace dynamics.

Anharmonic quantum mechanical systems do not feature phase space trajectories