Nonstationary perturbation theory for the energy shifts of a degenerate level
Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 2, pp. 219-229
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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.
@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 -
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/