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TMF, 1995, Volume 105, Number 2, Pages 246–255 (Mi tmf1372)  

This article is cited in 3 scientific papers (total in 3 papers)

Asymptotic of expansion of the evolution operator kernel in powers of time interval $\Delta t$

V. A. Slobodenyuk

Ul'yanovsk Branch of M. V. Lomonosov Moscow State University

Abstract: The upper bound for asymptotic behavior of the coefficients of expansion of the evolution operator kernel in powers of the time interval $\Delta t$ was obtained. It is found that for the nonpolynomial potentials the coefficients may increase as $n!$. But increasing may be more slow if the contributions with opposite signs cancel each other. Particularly, it is represented an example of the potential, for which the expansion converges. For the polynomial potentials $\Delta t$-expansion is certainly asymptotic one. The coefficients increase in this case as $\Gamma (n \frac {L-2}{L+2})$, where $L$ is the order of the polynom.

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English version:
Theoretical and Mathematical Physics, 1995, 105:2, 1387–1395

Bibliographic databases:

Received: 02.11.1994

Citation: V. A. Slobodenyuk, “Asymptotic of expansion of the evolution operator kernel in powers of time interval $\Delta t$”, TMF, 105:2 (1995), 246–255; Theoret. and Math. Phys., 105:2 (1995), 1387–1395

Citation in format AMSBIB
\Bibitem{Slo95}
\by V.~A.~Slobodenyuk
\paper Asymptotic of expansion of the evolution operator kernel in powers of time interval~$\Delta t$
\jour TMF
\yr 1995
\vol 105
\issue 2
\pages 246--255
\mathnet{http://mi.mathnet.ru/tmf1372}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1601141}
\zmath{https://zbmath.org/?q=an:0867.34069}
\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 105
\issue 2
\pages 1387--1395
\crossref{https://doi.org/10.1007/BF02070934}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995UP84300006}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Slobodenyuk, “Study of the convergence of the Schwinger–De Witt expansion for certain potentials”, Theoret. and Math. Phys., 109:1 (1996), 1302–1308  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Slobodenyuk, VA, “On convergence of the Schwinger-De Witt expansion”, Modern Physics Letters A, 12:37 (1997), 2889  crossref  mathscinet  zmath  adsnasa  isi
    3. Slobodenyuk, VA, “Potentials with convergent Schwinger-DeWitt expansion”, International Journal of Theoretical Physics, 37:6 (1998), 1753  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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