Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/53703
Type: Artigo de periódico
Title: A RIEMANN INTEGRAL APPROACH TO FEYNMANS PATH-INTEGRAL
Author: MONACO, RL
LAGOS, RE
RODRIGUES, WA
Abstract: 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.
Subject: PATH INTEGRALS
RIEMANN MEASURE
SCHRODINGER EQUATIONS
Editor: Plenum Publ Corp
Rights: fechado
Identifier DOI: 10.1007/BF02187816
Date Issue: 1995
Appears in Collections:Unicamp - Artigos e Outros Documentos

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