A PROBABILISTIC REPRESENTATION OF THE CAUCHY PROBLEM SOLUTION FOR THE MULTIDIMENSIONAL SCHROEDINGER EQUATION

P. N. Ievlev

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A PROBABILISTIC REPRESENTATION OF THE CAUCHY PROBLEM SOLUTION FOR THE MULTIDIMENSIONAL SCHROEDINGER EQUATION

机译：多维Schroedinger方程Cauchy问题解的概率表示。

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摘要

We construct a probabilistic representation of the Cauchy problem solution for the Schrodinger equation 2∂_tu = - △u. The result is an extension to the multidimensional case of the previous results by I. Ibragimov. N. Smorodina, and M. Faddeev.

机译：我们为Schrodinger方程2∂_tu=-△u构造了柯西问题解的概率表示。结果是对I. Ibragimov先前结果的多维情况的扩展。 N. Smorodina和M. Faddeev。

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《Journal of Mathematical Sciences 》 |2020年第5期| 796-804| 共9页
作者
P. N. Ievlev;
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St.Petersburg Department of the Steklov Mathematical Institute St.Petersburg State University St.Petersburg Russia;

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1. ON A LIMIT THEOREM RELATED TO PROBABILISTIC REPRESENTATION OF SOLUTION TO THE CAUCHY PROBLEM FOR THE SCHROEDINGER EQUATION [J] . I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev Journal of Mathematical Sciences . 2018 ,第6期

机译：关于SCHROEDINGER方程Cauchy问题解的概率表示的一个极限定理。
2. PROBABILISTIC REPRESENTATION OF A SOLUTION OF THE CAUCHY PROBLEM FOR EVOLUTION EQUATIONS WITH RIEMANN-LIOUVILLE OPERATORS [J] . Platonova M. V. Theory of probability and its applications . 2016 ,第3期

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3. A PROBABILISTIC REPRESENTATION OF SOLUTION TO THE CAUCHY PROBLEM FOR EVOLUTION EQUATION WITH DIFFERENTIAL OPERATOR OF ORDER GREATER THAN 2 [J] . M. V. Platonova Journal of Mathematical Sciences . 2018 ,第6期

机译：阶大于2的微分算子的演化方程Cauchy问题解的概率表示。
4. Finite time Blow up of solution of Cauchy problem for the multidimensional generalized double dispersion equations with arbitrary initial energy [C] . Wang Shuo, Yanbing Yang, Xu Runzhang 2011 International Conference on Multimedia Technology . 2011

机译：任意初始能量的多维广义双色散方程的柯西问题解的有限时间爆破
5. Existence and singularity of solutions for Cauchy problems of some partial differential equations. [D] . Song, Kyungwoo. 2002

机译：一类偏微分方程柯西问题解的存在性和奇异性。
6. New Integral Representations for Solutions of Cauchys Problem for Abstract Parabolic Equations [O] . J. A. Donaldson 1971

机译：抽象抛物方程的柯西问题解的新积分表示
7. Global existence and nonexistence of solution for Cauchy problem of multidimensional double dispersion equations [O] . Xu Runzhang, Liu Yacheng 2009

机译：多维双色散方程Cauchy问题解的整体存在性和不存在性
8. Exact Solutions of Multidimensional Schroedinger Equation with Polynomial Potentials [R] . Turbiner, A. V. , Ushveridze, A. G. 1986

机译：具有多项式势的多维schroedinger方程的精确解

A PROBABILISTIC REPRESENTATION OF THE CAUCHY PROBLEM SOLUTION FOR THE MULTIDIMENSIONAL SCHROEDINGER EQUATION

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