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TMF, 2004, Volume 141, Number 3, Pages 424–454 (Mi tmf131)  

This article is cited in 6 scientific papers (total in 6 papers)

Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb–Dirac Field

M. V. Karasev, E. M. Novikova

Moscow State Institute of Electronics and Mathematics

Abstract: The motion of a particle in the field of an electromagnetic monopole (in the Coulomb–Dirac field) perturbed by an axially symmetric potential after quantum averaging is described by an integrable system. Its Hamiltonian can be written in terms of the generators of an algebra with quadratic commutation relations. We construct the irreducible representations of this algebra in terms of second-order differential operators; we also construct its hypergeometric coherent states. We use these states in the first-order approximation with respect to the perturbing field to obtain the integral representation of the eigenfunctions of the original problem in terms of solutions of the model Heun-type second-order ordinary differential equation and present the asymptotic approximation of the corresponding eigenvalues.

Keywords: integrable systems, Dirac monopole, nonlinear commutation relations, coherent states, asymptotic spectrum behavior

DOI: https://doi.org/10.4213/tmf131

Full text: PDF file (413 kB)
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English version:
Theoretical and Mathematical Physics, 2004, 141:3, 1698–1724

Bibliographic databases:

Received: 12.04.2004

Citation: M. V. Karasev, E. M. Novikova, “Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb–Dirac Field”, TMF, 141:3 (2004), 424–454; Theoret. and Math. Phys., 141:3 (2004), 1698–1724

Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
\yr 2004
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\pages 1698--1724
\crossref{https://doi.org/10.1023/B:TAMP.0000049763.86662.16}
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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. Karasev M., “Birkhoff resonances and quantum ray method”, Days on Diffraction 2004, Proceedings, 2004, 114–126  crossref  isi
    2. M. V. Karasev, E. M. Novikova, “Algebra with polynomial commutation relations for the Zeeman effect in the Coulomb–Dirac field”, Theoret. and Math. Phys., 142:1 (2005), 109–127  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. M. V. Karasev, E. M. Novikova, “Algebra with polynomial commutation relations for the Zeeman–Stark effect in the hydrogen atom”, Theoret. and Math. Phys., 142:3 (2005), 447–469  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. A. V. Pereskokov, “Asymptotics of the Spectrum and Quantum Averages near the Boundaries of Spectral Clusters for Perturbed Two-Dimensional Oscillators”, Math. Notes, 92:4 (2012), 532–543  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. A. V. Pereskokov, “Asymptotics of the spectrum of the hydrogen atom in a magnetic field near the lower boundaries of spectral clusters”, Trans. Moscow Math. Soc., 73 (2012), 221–262  mathnet  crossref  mathscinet  zmath  elib
    6. A. V. Pereskokov, “Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters”, Izv. Math., 77:1 (2013), 163–210  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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