The~$1/n$ expansion in quantum mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 74 (1988) no. 3, pp. 399-411
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The classical approximation ($l=n-1\to\infty$) for the energy $\varepsilon^{(0)}$ and
the semiclassical expansion in problems of quantum mechanics are discussed. A recursive method is proposed for calculating the quantum corrections of arbitrary order
to $\varepsilon^{(0)}$, this being valid for both bound and quasistationary states. The generalization of the method to states with an arbitrary number of nodes and the
possibility of a more general choice of the parameter of the
semiclassical expansion are considered. The method is illustrated
by the example of the Yukawa and “funnel” potentials and for the
Stark effect in the hydrogen atom. These examples demonstrate
the rapid convergence of the $1/n$ expansion even for small quantum numbers.
@article{TMF_1988_74_3_a6,
author = {V. M. Vainberg and V. D. Mur and V. S. Popov and A. V. Sergeev and A. V. Shcheblykin},
title = {The~$1/n$ expansion in quantum mechanics},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {399--411},
publisher = {mathdoc},
volume = {74},
number = {3},
year = {1988},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1988_74_3_a6/}
}
TY - JOUR AU - V. M. Vainberg AU - V. D. Mur AU - V. S. Popov AU - A. V. Sergeev AU - A. V. Shcheblykin TI - The~$1/n$ expansion in quantum mechanics JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1988 SP - 399 EP - 411 VL - 74 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1988_74_3_a6/ LA - ru ID - TMF_1988_74_3_a6 ER -
%0 Journal Article %A V. M. Vainberg %A V. D. Mur %A V. S. Popov %A A. V. Sergeev %A A. V. Shcheblykin %T The~$1/n$ expansion in quantum mechanics %J Teoretičeskaâ i matematičeskaâ fizika %D 1988 %P 399-411 %V 74 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1988_74_3_a6/ %G ru %F TMF_1988_74_3_a6
V. M. Vainberg; V. D. Mur; V. S. Popov; A. V. Sergeev; A. V. Shcheblykin. The~$1/n$ expansion in quantum mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 74 (1988) no. 3, pp. 399-411. http://geodesic.mathdoc.fr/item/TMF_1988_74_3_a6/