Probabilistic Approximation
of the Evolution Operator e–itH where $H = \tfrac{{{{{( - 1)}}^{m}}}}{{(2m)!}}\tfrac{{{{d}^{{2m}}}}}{{d{{x}^{{2m}}}}}$
M. V. Platonovaa,b,* and S. V. Tcykina,**
a St. Petersburg Department, Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, 191023 Russia
b St. Petersburg State University, St. Petersburg,
199034 Russia
Correspondence to: *e-mail: mariyaplat@rambler.ru
Correspondence to: **e-mail: sergei.tcykin@gmail.com
Received 17 December, 2019
Abstract—Two approaches are suggested for constructing a probabilistic approximation of the evolution operator e–itH, where $H = \tfrac{{{{{( - 1)}}^{m}}}}{{(2m)!}}\tfrac{{{{d}^{{2m}}}}}{{d{{x}^{{2m}}}}}$, in the strong operator topology. In the first approach, the approximating operators have the form of expectations of functionals of a certain Poisson point field, while, in the second approach, the approximating operators have the form of expectations of functionals of sums of independent identically distributed random variables with finite moments of order 2m + 2.
Keywords: Schrödinger equation, Poisson random measures, limit theorems
DOI: 10.1134/S1064562420020192