RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (915 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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} 

• http://mi.mathnet.ru/eng/tmf1372
• http://mi.mathnet.ru/eng/tmf/v105/i2/p246

 SHARE:

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
2. Slobodenyuk, VA, “On convergence of the Schwinger-De Witt expansion”, Modern Physics Letters A, 12:37 (1997), 2889
3. Slobodenyuk, VA, “Potentials with convergent Schwinger-DeWitt expansion”, International Journal of Theoretical Physics, 37:6 (1998), 1753
•  Number of views: This page: 146 Full text: 44 References: 14 First page: 1