Classical mimics of quantum particle dynamics

Ehrenfest's theorem demonstrates that the expected values of the position and momentum for a quantum particle obey equations that correspond to the equations of motion for a classical particle. The correspondence is even stronger if one compares the equations for the quantum particle to the equations describing the motion of the centroid of a distribution of classical particles. Despite this correspondence, the trajectories followed in each case are typically quite different. In this talk---using the infinite square well as an example---we consider the question of when it is possible to construct a distribution of classical particles whose centroid follows a trajectory that does in fact match the trajectory of a quantum particle's expected position. We provide an explicit construction which leads to a condition on the initial quantum state for such a classical mimic to exist.