On a limit theorem related to probabilistic representation of solution to the Cauchy problem for the Schrödinger equation

DOI10.1007/s10958-018-3709-0zbMath1386.60087OpenAlexW2790386026MaRDI QIDQ1746407

I. A. Ibragimov, M. M. Faddeev, Nataliya V. Smorodina

Publication date: 25 April 2018

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-018-3709-0

zbMATH Keywords

random walkexponential momentunperturbed Schrödinger equation

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Random measures (60G57) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (8)

Antiquantization as a specific way from the statistical physics to the regular physics ⋮ Probabilistic representations for solutions to initial boundary value problems for non-stationary Schrödinger equation in \(d\)-hyperball ⋮ Approximation of the Evolution Operator by Expectations of Functionals of Sums of Independent Random Variables ⋮ Probabilistic Approximation of the Solution of the Cauchy Problem for the Higher-Order Schrödinger Equation ⋮ Probabilistic approximation of the evolution operator \(e^{-itH}\) where \(H = \frac{( - 1)^m}{(2m)!} \frac{d^{2m}}{dx^{2m}}\) ⋮ Reflecting Brownian motion in the \(d\)-ball ⋮ On one limit theorem related to the Cauchy problem solution for the Schrödinger equation with a fractional derivative operator of order \(\alpha \in \bigcup_{m=3}^{\infty}\left(m-1,m\right)\) ⋮ Probabilistic approximation of the evolution operator

Cites Work

• A complex analogue of the central limit theorem and a probabilistic approximation of the Feynman integral
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