Quantum Newton's law

Using the quantum Hamilton-Jacobi equation within the framework of the equi valence postulate, we construct a Lagrangian of a quantum system in one dim ension and derive a third-order equation of motion representing a first int egral of the quantum Newton's law. We then integrate this equation in the f ree particle case and compare our results to those of Floydian trajectories . Finally, we propose a quantum version of Jacobi's theorem. (C) 2001 Elsev ier Science B.V. All rights reserved.