A probabilistic approach to semi-classical approximations

Gérard Ben Arous, Fabienne Castell

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Abstract

We study in this paper the semi-classical expansion of the Schrödinger equation, using a probabilistic approach based on the Wiener measure. Using almost-analytic extensions, we exhibit a probabilistic ansatz for the wave function. We show that this ansatz approximates very well the wave function in the semi-classical regime, and gives the semi-classical expansion under mild hypothesis on the potential at infinity, and no analyticity conditions. In this paper, the study takes place before the caustics.

Original languageEnglish (US)
Pages (from-to)243-280
Number of pages38
JournalJournal of Functional Analysis
Volume137
Issue number1
DOIs
StatePublished - Apr 10 1996

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ASJC Scopus subject areas

  • Analysis

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