Geodesic
Asymptotic of expansion of the evolution operator kernel in powers of time interval~$\Delta t$
Teoretičeskaâ i matematičeskaâ fizika, Tome 105 (1995) no. 2, pp. 246-255

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_1995_105_2_a5,
     author = {V. A. Slobodenyuk},
     title = {Asymptotic of expansion of the evolution operator kernel in powers of time interval~$\Delta t$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {246--255},
     publisher = {mathdoc},
     volume = {105},
     number = {2},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_105_2_a5/}
}
TY  - JOUR
AU  - V. A. Slobodenyuk
TI  - Asymptotic of expansion of the evolution operator kernel in powers of time interval~$\Delta t$
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1995
SP  - 246
EP  - 255
VL  - 105
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1995_105_2_a5/
LA  - ru
ID  - TMF_1995_105_2_a5
ER  - 
%0 Journal Article
%A V. A. Slobodenyuk
%T Asymptotic of expansion of the evolution operator kernel in powers of time interval~$\Delta t$
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1995
%P 246-255
%V 105
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1995_105_2_a5/
%G ru
%F TMF_1995_105_2_a5
V. A. Slobodenyuk. Asymptotic of expansion of the evolution operator kernel in powers of time interval~$\Delta t$. Teoretičeskaâ i matematičeskaâ fizika, Tome 105 (1995) no. 2, pp. 246-255. http://geodesic.mathdoc.fr/item/TMF_1995_105_2_a5/