This article is cited in 4 papers

Integrable dynamical systems generated by quantum models with an adiabatic parameter

A. Mylläri^ab, S. Yu. Slavyanov<sup>c

a</sup> Åbo Akademi University, Turku, Finland
^b University of Turku, Turku, Finland
^c St.~Petersburg State University, Russia

Abstract: 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.

Received: 04.09.2010

DOI: 10.4213/tmf6607

 English version: Theoretical and Mathematical Physics, 2011, 166:2, 224–227

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