Abstract
For a wave packet evolving quantum mechanically, the rates of change of the expectations and uncertainties of the position and momentum are exactly the same as if Wigner's function instantaneously obeyed a classical Liouville equation (whatever the Hamiltonian). This extension of Ehrenfest's theorem should be useful for dealing with the evolution and manipulation of quantum states.
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Royer, A. Ehrenfest's theorem reinterpreted and extended with Wigner's function. Found Phys 22, 727–736 (1992). https://doi.org/10.1007/BF01889675
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DOI: https://doi.org/10.1007/BF01889675