The classical action in nonrelativistic quantum mechanics

Aubrey Truman

Research output: Contribution to journalArticle

Abstract

We obtain some new results on the role played by the classical action in nonrelativistic quantum mechanics. The results are of the same genre as those derived previously by Nelson from the Trotter product formula. Here we work with the exact expression for the classical action not the approximate one as used by Nelson. Our results give a precise relationship between classical mechanics and quantum mechanics for a fairly wide class of potentials. The results are derived by using the properties of a new definition of the Feynman path integral J introduced in an earlier paper. Copyright © 1977 American Institute of Physics.

Original languageEnglish
Pages (from-to)1499-1509
Number of pages11
JournalJournal of Mathematical Physics
Volume18
Issue number7
Publication statusPublished - 1976

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Truman, Aubrey. / The classical action in nonrelativistic quantum mechanics. In: Journal of Mathematical Physics. 1976 ; Vol. 18, No. 7. pp. 1499-1509.
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The classical action in nonrelativistic quantum mechanics. / Truman, Aubrey.

In: Journal of Mathematical Physics, Vol. 18, No. 7, 1976, p. 1499-1509.

Research output: Contribution to journalArticle

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AB - We obtain some new results on the role played by the classical action in nonrelativistic quantum mechanics. The results are of the same genre as those derived previously by Nelson from the Trotter product formula. Here we work with the exact expression for the classical action not the approximate one as used by Nelson. Our results give a precise relationship between classical mechanics and quantum mechanics for a fairly wide class of potentials. The results are derived by using the properties of a new definition of the Feynman path integral J introduced in an earlier paper. Copyright © 1977 American Institute of Physics.

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