TY - JOUR
T1 - A probabilistic approach to semi-classical approximations
AU - Ben Arous, Gérard
AU - Castell, Fabienne
PY - 1996/4/10
Y1 - 1996/4/10
N2 - 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.
AB - 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.
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U2 - 10.1006/jfan.1996.0046
DO - 10.1006/jfan.1996.0046
M3 - Article
AN - SCOPUS:0030577873
SN - 0022-1236
VL - 137
SP - 243
EP - 280
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -