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A Probabilistic Approximation of the Cauchy Problem Solution for the Schrödinger Equation with a Fractional Derivative Operator

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We construct two types of probabilistic approximations of the Cauchy problem solution for the nonstationary Schrödinger equation with a symmetric fractional derivative of order α ∈ (1, 2) at the right-hand side. In the first case, we approximate the solution by mathematical expectation of point Poisson field functionals, and in the second case, we approximate the solution by mathematical expectation of functionals of sums of independent random variables having a power asymptotics of a tail distribution.

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Correspondence to M. V. Platonova.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 466, 2017, pp. 257–272.

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Platonova, M.V., Tsykin, S.V. A Probabilistic Approximation of the Cauchy Problem Solution for the Schrödinger Equation with a Fractional Derivative Operator. J Math Sci 244, 874–884 (2020) doi:10.1007/s10958-020-04659-7

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