The existence of nonvanishing Bohm potentials, in the Madelung-Bohm version of the Schrödinger equation, allows for the construction of particular solutions for states of quantum particles interacting with nontrivial external potentials that propagate as free classical particles. Such solutions are constructed with phases which satisfy the classical Hamilton-Jacobi for free particles and whose probability densities propagate with constant velocity, as free classical particles do.

• Received 4 July 2020
• Accepted 23 October 2020

DOI:https://doi.org/10.1103/PhysRevA.102.052211