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 (Unpublished)

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## Abstract

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 |
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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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