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Zap. Nauchn. Sem. POMI, 2017, Volume 466, Pages 145–158 (Mi znsl6547)  

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

P. N. Ievlevab

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

Funding Agency Grant Number
Russian Science Foundation 17-11-01136


Full text: PDF file (200 kB)
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Document Type: Article
UDC: 519.2
Received: 31.10.2017

Citation: P. N. Ievlev, “Probabilistic representation of the Cauchy problem solution for the multidimensional Shrödinger equation”, Probability and statistics. Part 26, Zap. Nauchn. Sem. POMI, 466, POMI, St. Petersburg, 2017, 145–158

Citation in format AMSBIB
\Bibitem{Iev17}
\by P.~N.~Ievlev
\paper Probabilistic representation of the Cauchy problem solution for the multidimensional Shr\"odinger equation
\inbook Probability and statistics. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 466
\pages 145--158
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6547}


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