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TMF, 2011, Volume 166, Number 2, Pages 261–265 (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

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

DOI: https://doi.org/10.4213/tmf6607

Full text: PDF file (306 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 166:2, 224–227

Bibliographic databases:

Received: 04.09.2010

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. Yu. Slavyanov, “Derivation of Painlevé equations by antiquantization”, Painlevé equations and related topics, Degruyter Proceedings in Mathematics, Walter de Gruyter, Berlin, 2012, 253–256  mathscinet  isi
    2. S. Y. Slavyanov, “Relations between linear equations and Painlevé's equations”, Constr. Approx., 39:1 (2014), 75–83  crossref  mathscinet  zmath  isi  scopus
    3. S. Yu. Slavyanov, “Antiquantization and the corresponding symmetries”, Theoret. and Math. Phys., 185:1 (2015), 1522–1526  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. Ishkhanyan A.M., “A singular Lambert-$W$ Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions”, Mod. Phys. Lett. A, 31:33 (2016), 1650177  crossref  mathscinet  zmath  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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