P. N. Ievlev, “Probabilistic representation of the Cauchy problem solution for the multidimensional Shrödinger equation”, Zap. Nauchn. Sem. POMI, 2017, Volume 466,Pages <nobr>145

This article is cited in 5 papers

Probabilistic representation of the Cauchy problem solution for the multidimensional Shrödinger equation

P. N. Ievlev^ab

^a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
^b St. Petersburg State University, St. Petersburg, Russia

Abstract: We construct a probabilistic representation of the Cauchy problem solution for the Shrödinger equation $2i\partial_tu=-\Delta u$. The result is an extension to a mulidimensional case of the previous results by I. Ibragimov, N. Smorodina and M. Faddeev.

Key words and phrases: limit theorems, Schrödinger equation, Feynman measure, evolution equations.

UDC: 519.2

Received: 31.10.2017