Feynman path integrals for polynomially growing potentials

Albeverio, Sergio and Mazzucchi, Sonia (2003) Feynman path integrals for polynomially growing potentials. UNSPECIFIED. (Unpublished)

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    A general class of infinite dimensional oscillatory integrals with polynomially growing phase functions is studied. A representation formula of the Parseval type is proved, as well as a formula giving the integrals in terms of analytically continued absolutely convergent integrals. These results are applied to provide a rigorous Feynman path integral representation for the solution of the time dependent Schrödinger equation with a quartic anharmonial potential. The Borel summability of the asymptotic expansion of the solution in power series of the coupling constant is also proved.

    Item Type: Departmental Technical Report
    Department or Research center: Mathematics
    Subjects: Q Science > QC Physics (General) > QC174.2 Schrodinger Equation
    Q Science > QC Physics (General) > QC174.17.P27 Integrals, path
    Uncontrolled Keywords: Feynman path integrals - Schrödinger equation - quartic oscillator potential - asymptotic expansion
    Report Number: UTM 638, March 2003
    Repository staff approval on: 17 May 2005

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