caa a22 4500 46794508X CHVBK 20180405193736.0 cr unu---uuuuu 170328e20050101xx s 000 0 eng 10.1007/s11232-005-0074-1 doi (NATIONALLICENCE)springer-10.1007/s11232-005-0074-1 (NATIONALLICENCE)springer-10.1007/s11232-005-0012-2 Algebra with polynomial commutation relations for the Zeeman effect in the Coulomb-Dirac field [Elektronische Daten] [M. Karasev, E. Novikova] We consider a model of particle motion in the field of an electromagnetic monopole (in the Coulomb-Dirac field) perturbed by homogeneous and inhomogeneous electric fields. After quantum averaging, we obtain an integrable system whose Hamiltonian can be expressed in terms of the generators of an algebra with polynomial commutation relations. We construct the irreducible representations of this algebra and its hypergeometric coherent states. We use these states to represent the eigenfunctions of the original problem in terms of the solutions of the model ordinary differential equation. We also present the asymptotic approximations of the eigenvalues in the leading term of the perturbation theory, where the degeneration of the spectrum is removed completely. Springer Science+Business Media, Inc., 2005 asymptotic behavior of spectrum nationallicence integrable systems nationallicence Dirac monopole nationallicence nonlinear commutation relations nationallicence coherent states nationallicence asymptotic behavior ofsp ectrum nationallicence Karasev M. Moscow Institute of Electronics and Mathematics, Moscow, Russia aut Novikova E. Moscow Institute of Electronics and Mathematics, Moscow, Russia aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 142/1(2005-01-01), 109-127 0040-5779 142:1<109 2005 142 11232 https://doi.org/10.1007/s11232-005-0074-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-005-0074-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Karasev M. Moscow Institute of Electronics and Mathematics, Moscow, Russia aut NATIONALLICENCE 700 1- Novikova E. Moscow Institute of Electronics and Mathematics, Moscow, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 142/1(2005-01-01), 109-127 0040-5779 142:1<109 2005 142 11232 NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-005-0012-2 text/html Onlinezugriff via DOI Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 466871295 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE NATIONALLICENCE NL-springer