Geodesic
Integrable dynamical systems generated by quantum models with an adiabatic parameter
Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 2, pp. 261-265 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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, integrable dynamical system.
Mots-clés : Painlevé equation 
@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},
     year = {2011},
     volume = {166},
     number = {2},
     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
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
%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/

[1] C. L. Charlier, Die Mechanik des Himmels, Walter de Gruyter, Berlin, 1927 | Zbl

[2] I. V. Komarov, L. I. Ponomarev, S. Yu. Slavyanov, Sferoidalnye i kulonovskie sferoidalnye funktsii, Nauka, M., 1975 | MR

[3] L. Euler, “Problème: un corps étant attiré en raison réciproque quarée des distances vers deux points fixes donnés, trouver les cas ou la courbe décrite par ce corps sera algébrique”, Mémoires de l'académie des sciences de Berlin, v. XVI, 1767, 228–249 ; Commentationes mechanicae ad theoriam motus punctorum pertinentes, Opera Omnia. Ser. 2. Opera Mechanica et Astronomica, 6, Soc. Sci. Natur. Helv., Lausanne, 1764, 209–293 | MR | Zbl

[4] I. A. Gerasimov, Zadacha dvukh nepodvizhnykh tsentrov L. Eilera, Vek 2, Fryazino, 2007

[5] A. S. Fokas, A. R. Its, A. A. Kapaev, V. Yu. Novokshenov, Painlevé Transcendents: a Riemman–Gilbert Approach, Math. Surv. Monogr., 128, AMS, Providence, RI, 2006 | DOI | MR | Zbl

[6] V. I. Gromak, I. Laine, S. Shimomura, Painlevé Differential Equations in the Complex Plane, de Gruyter Stud. Math., 28, de Gruyter, Berlin, 2002 | DOI | MR | Zbl

[7] S. Yu. Slavyanov, F. R. Vukailovich, TMF, 150:1 (2007), 143–151 | DOI | MR | Zbl

[8] S. Slavyanov, V. Lai, Spetsialnye funktsii: edinaya teoriya, osnovannaya na analize osobennostei, Nevskii dialekt, SPb., 2002