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We propose a new method to evaluate the effective potential in the pathintegral for the fixed-energy amplitude as well as for the pseudotime evolutionkernel in the formalism by Duru and Kleinert. Restriction to the postpoint orthe prepoint prescriptions in formulating time sliced path integrals is avoidedby leaving off the use of expectation values for correction terms. This enablesus to consider an arbitrary ordering prescription and to examine the orderingdependence of the effective potential. To investigate parameter dependences, weintroduce the ordering parameter $\alpha$ in addition to the splittingparameter $\lambda$ in the formulation of the time sliced path integral. Theresulting path integrals are found to be independent of the ordering parameteralthough the explicit dependence, given by a contribution proportional to$(1-2\lambda)^{2}$, on the splitting parameter remains. As an application, wecheck the relationship between path integrals for the radial oscillator and theradial Coulomb system in arbitrary dimensions.

On the effective potential of Duru-Kleinert path integrals