Ehrenfest Theorem for the Hamilton--Jacobi Equation

L. Kocis Peranga Court, Unit 4, 43 Fifth Av., Sandgate QLD 4017, Australia

Received: July 3, 2002

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A possible way from quantum mechanics to classical mechanics can be achieved with an exponential substitution used in the Schrödinger equation, and then considering the classical limit. This gives a picture of classical fluid 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.

DOI: 10.12693/APhysPolA.102.709 PACS numbers: 03.65.Bz