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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 466, Pages 145–158 (Mi znsl6547)  
This article is cited in 5 scientific papers (total in 5 papers)

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
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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
Received: 31.10.2017
Document Type: Article
UDC: 519.2
Language: Russian
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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  • https://www.mathnet.ru/eng/znsl/v466/p145
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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