Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 2, pp. 219-229
Citer cet article
A. N. Vasil'ev; A. L. Kitanin. Nonstationary perturbation theory for the energy shifts of a degenerate level. Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 2, pp. 219-229. http://geodesic.mathdoc.fr/item/TMF_1975_24_2_a7/
@article{TMF_1975_24_2_a7,
author = {A. N. Vasil'ev and A. L. Kitanin},
title = {Nonstationary perturbation theory for the energy shifts of a~degenerate level},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {219--229},
year = {1975},
volume = {24},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1975_24_2_a7/}
}
TY - JOUR
AU - A. N. Vasil'ev
AU - A. L. Kitanin
TI - Nonstationary perturbation theory for the energy shifts of a degenerate level
JO - Teoretičeskaâ i matematičeskaâ fizika
PY - 1975
SP - 219
EP - 229
VL - 24
IS - 2
UR - http://geodesic.mathdoc.fr/item/TMF_1975_24_2_a7/
LA - ru
ID - TMF_1975_24_2_a7
ER -
%0 Journal Article
%A A. N. Vasil'ev
%A A. L. Kitanin
%T Nonstationary perturbation theory for the energy shifts of a degenerate level
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1975
%P 219-229
%V 24
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1975_24_2_a7/
%G ru
%F TMF_1975_24_2_a7
The asymptotic (when $T\equiv t_1-t_2\to\infty$ ) representation for the operator $PS(t_1,t_2)P$ where $P$ is the projector on some degenerate subspace of the nonperturbed energy level and $S(t_1,t_2)$ is the operator of the time development in the interaction picture is obtained. The asymptotic formula is the following: $$PS(t_1,t_2)P=R_0\exp (-iQT)=(\exp\{-iQ^+T\})R_0=R_0^{1/2}(\exp\{-i\bar QT\})R_0^{1/2},$$ where $Q$ is the nonhermitian secular operator [3], $R_0$ and $\bar Q$ are the hermitian operators.
