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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 166, Number 2, Pages 261–265
DOI: https://doi.org/10.4213/tmf6607 (Mi tmf6607) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Integrable dynamical systems generated by quantum models with an adiabatic parameter

A. Mylläriab, S. Yu. Slavyanovc

a Åbo Akademi University, Turku, Finland
b University of Turku, Turku, Finland
c St.~Petersburg State University, Russia
Full-text PDF (306 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf6607
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
English version:
Theoretical and Mathematical Physics, 2011, Volume 166, Issue 2, Pages 224–227
DOI: https://doi.org/10.1007/s11232-011-0016-z
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. Mylläri, S. Yu. Slavyanov, “Integrable dynamical systems generated by quantum models with an adiabatic parameter”, TMF, 166:2 (2011), 261–265; Theoret. and Math. Phys., 166:2 (2011), 224–227
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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