Ehrenfest Theorem for the Hamilton-Jacobi Equation

• Authors: L. Kocis
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

03.65.Bz  

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2002
• Volume: 102
• Issue: 6
• Pages: 709-716

Dates

published

2002-12

received

2002-07-03

References

• 1. D.I. Davydov, Quantum Mechanics, Pergamon, New York 1965, p. 49
• 2. D.I. Blokhintsev, Quantum Mechanics, Reidel, Dordrecht 1964, p. 102
• 3. L.E. Ballentine, Y.M. Yang, J.P. Zibin, Phys Rev. A, 50, 2854, 1994
• 4. A. Messiah, Quantum Mechanics, Vol. 1, North-Holland, Amsterdam 1961, p. 222
• 5. L.E. Ballentine, J.P. Zibin, Phys. Rev. A, 54, 3813, 1996
• 6. L.E. Ballentine, S.M. McRae, Phys. Rev. A, 58, 1799, 1998
• 7. L. Kocis, Acta Phys. Pol. A, 101, 213, 2002

Identifiers

DOI

10.12693/APhysPolA.102.709