Ehrenfest Theorem for the Hamilton-Jacobi Equation

Abstract

A possible way from quantum mechanics to classical mechanics can be achieved with an exponential substitution used in the Schrodinger equation, and then considering the classical limit. This gives a picture of classicalfluid and an ensemble of classical trajectories. In difference from this approach to the classical limit, while utilising the same substitution, we assume a minimum uncertainty wave packet. It is shown that this approach to the classical limit of quantum mechanics yields a single trajectory traced by the centroid of the minimum uncertainty wave packet. The momentum and the centroid of such packet satisfy the classical Hamilton-Jacobi equation.