L’équation de Schrödinger quand h tend vers zero: une approche probabiliste. (French) Zbl 0555.60040

Azencott, R.; Doss, H.

Stochastic aspects of classical and quantum systems, Proc. 2nd French- German Encounter Math. Phys., Marseille 1983, Lect. Notes Math. 1109, 1-17 (1985).

[For the entire collection see Zbl 0546.00037.]
Starting from an analytic extension of the Feynman-Kac formula and via an appropriate extension of the Cameron-Martin formula, the authors obtain an asymptotic expansion of the solution of Schrödinger’s equation as Planck’s constant tends to zero. The result is contained in Theorem (3.14) where also a probabilistic expression is provided for the different terms of the expansion.

Reviewer: H.Gzyl

MSC:

60H25	Random operators and equations (aspects of stochastic analysis)
60F99	Limit theorems in probability theory

Keywords:

Feynman-Kac formula; Cameron-Martin formula; Schrödinger’s equation

Citations:

Zbl 0546.00037