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arXiv.org e-Print Archive
Preprint . 2012
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Derivation of the Schr\"odinger equation from the Hamilton-Jacobi equation in Feynman's path integral formulation of quantum mechanics

descriptionPublicationkeyboard_double_arrow_right Preprint 03 Apr 2012
Authors: Field, J. H.;

arXiv: 1204.0653

Derivation of the Schr\"odinger equation from the Hamilton-Jacobi equation in Feynman's path integral formulation of quantum mechanics

Abstract

It is shown how the time-dependent Schr\"{o}dinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schr\"{o}dinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi equation, are also reviewed. The derivation of the time-dependent equation is based on an {\it a priori} assumption equivalent to Feynman's dynamical postulate. De Broglie's concepts of 'matter waves' and their phase and group velocities are also critically discussed.

Comment: 30 pages, no figures, no tables

Keywords

Physics - General Physics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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