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

Authors: Pavel Ievlev

Published in: Zap. Nauchn. Sem. POMI (2017)

Date: January 2017

Abstract

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

BibTeX

@article {MR3760049,
    AUTHOR = {Ievlev, P. N.},
    TITLE = {Probabilistic representation of the solution of the {C}auchy problem for the multidimensional {S}chr\"odinger equation},
   JOURNAL = {Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov.              (POMI)},
   FJOURNAL = {Rossi\u iskaya Akademiya Nauk. Sankt-Peterburgskoe Otdelenie.              Matematicheski\u i\ Institut im. V. A. Steklova. Zapiski Nauchnykh Seminarov (POMI)},
   VOLUME = {466},
   YEAR = {2017},
   PAGES = {145--158},
   ISSN = {0373-2703},
   MRCLASS = {60H30 (35C05 35C15 35Q41)},
   MRNUMBER = {3760049}
}