Abstract
A method for approximation of the operator e−itH, where \(H = - \frac{1}{2}\frac{{{d^2}}}{{d{x^2}}} + V(x)\), in the strong operator topology is proposed. The approximating operators have the form of expectations of functionals of a certain random point field.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 52, No. 2, pp. 25–39, 2018
Original Russian Text Copyright © by I. A. Ibragimov, N. V. Smorodina, and M. M. Faddeev
I. A. Ibragimov acknowledges the financial support of the Russian Foundation for Basic Research (project no. 16-01-00258). N. V. Smorodina (who authors the results of Section 3) acknowledges the support of the Russian Science Foundation (project no. 17-11-01136). M. M. Faddeev (who authors the results of Section 4) acknowledges the support of the Russian Science Foundation (project no. 17-11-01136).
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Ibragimov, I.A., Smorodina, N.V. & Faddeev, M.M. Probabilistic Approximation of the Evolution Operator. Funct Anal Its Appl 52, 101–112 (2018). https://doi.org/10.1007/s10688-018-0216-5
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DOI: https://doi.org/10.1007/s10688-018-0216-5