The classical action in nonrelativistic quantum mechanics

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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 ℱ introduced in an earlier paper.

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