M. V. Platonova, “An analogue of the Feynman–Kac formula for the multidimensional Shrödinger equation”, Zap. Nauchn. Sem. POMI, 2023, Volume 525,Pages <nobr>96

An analogue of the Feynman–Kac formula for the multidimensional Shrödinger equation

M. V. Platonova^ab

^a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
^b Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: A probabilistic approximation of the solution of the Cauchy problem for the multidimensional Schrödinger equation with limited potential is constructed. The approximation has the form of expectations of functionals of a random point field.

Key words and phrases: Schrödinger equation, Poisson random measure, Feynman–Kac formula.

MSC: 28C20, 60H05, 60G57

Received: 04.10.2023