Integrable dynamical systems generated by quantum models with an~adiabatic parameter
Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 2, pp. 261-265
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Several models solvable in terms of special functions of the Heun class are widely used in quantum mechanics. They are all characterized by the presence of a parameter that can be regarded as an adiabatic variable. An antiquantization procedure applied to such a model generates a dynamical model with properties of the Painlevé equations. The mentioned parameter plays the role of time. We consider examples of such models.
Keywords:
two-Coulomb-center problem, Stark effect in hydrogen, Painlevé equation, integrable dynamical system.
@article{TMF_2011_166_2_a4,
author = {A. Myll\"ari and S. Yu. Slavyanov},
title = {Integrable dynamical systems generated by quantum models with an~adiabatic parameter},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {261--265},
publisher = {mathdoc},
volume = {166},
number = {2},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2011_166_2_a4/}
}
TY - JOUR AU - A. Mylläri AU - S. Yu. Slavyanov TI - Integrable dynamical systems generated by quantum models with an~adiabatic parameter JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2011 SP - 261 EP - 265 VL - 166 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2011_166_2_a4/ LA - ru ID - TMF_2011_166_2_a4 ER -
%0 Journal Article %A A. Mylläri %A S. Yu. Slavyanov %T Integrable dynamical systems generated by quantum models with an~adiabatic parameter %J Teoretičeskaâ i matematičeskaâ fizika %D 2011 %P 261-265 %V 166 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2011_166_2_a4/ %G ru %F TMF_2011_166_2_a4
A. Mylläri; S. Yu. Slavyanov. Integrable dynamical systems generated by quantum models with an~adiabatic parameter. Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 2, pp. 261-265. http://geodesic.mathdoc.fr/item/TMF_2011_166_2_a4/