We construct a probabilistic representation of the Cauchy problem solution for the Schrödinger equation 2i∂tu = − Δu. The result is an extension to the multidimensional case of the previous results by I. Ibragimov, N. Smorodina, and M. Faddeev.
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I. A. Ibragimov, N. V. Smorodina, and M. M. Faddeev, “On a limit theorem related to the probabilistic representation of the solution of the Cauchy problem for the Schrödinger equation,” Zap. Nauchn. Semin. POMI, 454, 158–176 (2016).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 466, 2017, pp. 145–158.
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Ievlev, P.N. A Probabilistic Representation of the Cauchy Problem Solution for the Multidimensional Schrödinger Equation. J Math Sci 244, 796–804 (2020) doi:10.1007/s10958-020-04653-z