Albeverio, S. and Mazzucchi, S. (2009) An Asymptotic Functional-Integral solution for the Schrödinger Equation with Polynomial Potential. UNSPECIFIED. (Unpublished)
Abstract
A functional integral representation for the weak solution of the Schrödinger equation with a polynomially growing potential is proposed in terms of an analytically continued Wiener integral. The asymptotic expansion in powers of the coupling constant λ of the matrix elements of the Schrödinger group is studied and its Borel summability is proved.
| Item Type: | Departmental Technical Report |
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| Department or Research center: | Mathematics |
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| Subjects: | UNSPECIFIED |
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| Uncontrolled Keywords: | Feynman path integrals, Schrödinger equation, analytic continuation of Wiener integrals, polynomial potential, asymptotic expansions. |
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| Additional Information: | AMS classification : 35C15, 35Q40, 35C20, 34M30, 28C20, 47D06, 35B60. |
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| Report Number: | UTM 727, January 2009 |
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| Repository staff approval on: | 30 Jan 2009 |
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