It is shown that under certain conditions the time-dependent Hamilton–Jacobi equation (TDHJE) is satisfied in the mean in quantum mechanics provided the classical action is replaced by Dirac's complex quantal action. This may be regarded as the equivalent of Ehrenfest's theorem for the TDHJE. Expectation values of operators are discussed in a similar manner.

Bibliography

1 E. Schrödinger, Ann. Physik [4], 79, 361 (1926).
10.1002/andp.19263840404
Google Scholar
2 E. Schrödinger, Ann. Physik [4], 79, 489 (1926).
10.1002/andp.19263840602
Google Scholar
3 G. Wentzel, Z. Physik, 38, 518 (1926).
10.1007/BF01397171
Web of Science® Google Scholar
4 L. Brillouin, Compt. Rend. 183, 24 (1926).
Web of Science® Google Scholar
5 L. Brillouin, J. Phys. 7, 353 (1926).
Web of Science® Google Scholar
6 C. Eckart, Proc. Natl. Acad. Sci. U.S. 12, 684 (1926).
10.1073/pnas.12.12.684
CAS PubMed Web of Science® Google Scholar
7 J. H. Van Vleck, Proc. Natl. Acad. Sci. U.S. 14, 178 (1928).
10.1073/pnas.14.2.178
CAS PubMed Google Scholar
8 W. Pauli, Handbuch der Physik, 2nd edn. (Springer-Verlag, Berlin, 1933), Vol. 24/1, pp. 166–170.
Google Scholar
9 R. C. Tolman, Statistical Mechanics (Oxford University Press, London, 1938), pp. 243–245.
Google Scholar
10 P. A. M. Dirac, Quantum Mechanics, 4th edn. (Oxford University Press, London, 1958), pp. 121–130.
Google Scholar
11 R. Schiller, Phys. Rev. 125, 1100, 1109 (1962).
10.1103/PhysRev.125.1100
Web of Science® Google Scholar
12 L. Motz, Phys. Rev. 126, 378 (1962).
10.1103/PhysRev.126.378
Web of Science® Google Scholar
13 Y. Nishiyama, Progr. Theoret. Phys. (Kyoto) 30, 657 (1963).
10.1143/PTP.30.657
Web of Science® Google Scholar
14 L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon Press, Oxford, 1960), pp. 22–24.
Google Scholar
15 R. Abrines and I. C. Percival, Proc. Phys. Soc. (London) 88, 893 (1966).
10.1088/0370-1328/88/4/309
Web of Science® Google Scholar
16 R. D. Levine and B. R. Johnson, Chem. Phys. Letters, 7, 404 (1970).
10.1016/0009-2614(70)80319-0
CAS Web of Science® Google Scholar
17 L. I. Schiff, Quantum Mechanics, 3rd edn. (McGraw-Hill, New York, 1968), p. 49.
Google Scholar
18 W. J. Taylor, Int. J. Quantum Chem. 2, 735 (1968).
10.1002/qua.560020513
CAS Google Scholar
19 P. Ehrenfest, Z. Physik, 45, 455 (1927).
10.1007/BF01329203
Google Scholar
20 H. Weyl, Z. Physik, 46, 1 (1927).
10.1007/BF02055756
Google Scholar
21 N. H. McCoy, Proc. Natl. Acad. Sci. U.S. 18, 674 (1932).
10.1073/pnas.18.11.674
CAS PubMed Google Scholar

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Volume6, Issue3

May 1972

Pages 449-453

On the validity of Hamilton-Jacobi mechanics in the mean in quantum mechanics

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On the validity of Hamilton-Jacobi mechanics in the mean in quantum mechanics

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