A RIEMANN INTEGRAL APPROACH TO FEYNMANS PATH-INTEGRAL
Contribuinte(s) |
Universidade Estadual Paulista (UNESP) |
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Data(s) |
20/05/2014
20/05/2014
01/08/1995
|
Resumo |
It is a well known result that the Feynman's path integral (FPI) approach to quantum mechanics is equivalent to Schrodinger's equation when we use as integration measure the Wiener-Lebesgue measure. This results in little practical applicability due to the great algebraic complexibity involved, and the fact is that almost all applications of (FPI) - ''practical calculations'' - are done using a Riemann measure. In this paper we present an expansion to all orders in time of FPI in a quest for a representation of the latter solely in terms of differentiable trajetories and Riemann measure. We show that this expansion agrees with a similar expansion obtained from Schrodinger's equation only up to first order in a Riemann integral context, although by chance both expansions referred to above agree for the free. particle and harmonic oscillator cases. Our results permit, from the mathematical point of view, to estimate the many errors done in ''practical'' calculations of the FPI appearing in the literature and, from the physical point of view, our results supports the stochastic approach to the problem. |
Formato |
365-373 |
Identificador |
http://dx.doi.org/10.1007/BF02187816 Foundations of Physics Letters. New York: Plenum Publ Corp, v. 8, n. 4, p. 365-373, 1995. 0894-9875 http://hdl.handle.net/11449/31534 10.1007/BF02187816 WOS:A1995RT72700005 |
Idioma(s) |
eng |
Publicador |
Plenum Publ Corp |
Relação |
Foundations of Physics Letters |
Direitos |
closedAccess |
Palavras-Chave | #PATH INTEGRALS #RIEMANN MEASURE #SCHRODINGER EQUATIONS |
Tipo |
info:eu-repo/semantics/article |