Study of the convergence of the Schwinger--De Witt expansion for certain potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 1, pp. 70-79
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It is established that Schwinger–de Witt expansion is convergent for the potential $V=q^2/2+g/q^2$ (here $g=\lambda(\lambda-1)/2$ and $\lambda$ is integer number) and for a number of three-dimensional potentials with separated variables, but is divergent for the potentials $V=qe^{aq}$, $V=-ge^{-a^2q^2}$. Thereby it is shown that the initial condition for the evolution operator kernel for two latter potentials is fulfilled only in asymptotic sense. An outstanding role of the potentials for which Schwinger–de Witt expansion converges is discussed.
@article{TMF_1996_109_1_a6,
author = {V. A. Slobodenyuk},
title = {Study of the convergence of the {Schwinger--De} {Witt} expansion for certain potentials},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {70--79},
publisher = {mathdoc},
volume = {109},
number = {1},
year = {1996},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a6/}
}
TY - JOUR AU - V. A. Slobodenyuk TI - Study of the convergence of the Schwinger--De Witt expansion for certain potentials JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1996 SP - 70 EP - 79 VL - 109 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a6/ LA - ru ID - TMF_1996_109_1_a6 ER -
V. A. Slobodenyuk. Study of the convergence of the Schwinger--De Witt expansion for certain potentials. Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 1, pp. 70-79. http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a6/