In classical physics, phase space trajectories give rise to flow-fields representing the dynamics of the system along its trajectories; they yield additional insight into a system’s behavior.

Quantum theory phase space trajectories do not exist because Heisenberg’s uncertainty principle does not allow for the formation of sharply defined trajectories. But quantum physicists have not given up entirely on phase space, and so the study of the next best thing, the movement of quantum physics’ phase space-based probability distributions, has actually boomed in recent years.
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