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Title: Flensted-Jensen's functions attached to the Landau problem on the hyperbolic disc (English)
Author: Mouayn, Zouhaïr
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 52
Issue: 2
Year: 2007
Pages: 97-104
Summary lang: English
Category: math
Summary: We give an explicit expression of a two-parameter family of Flensted-Jensen’s functions $\Psi _{\mu ,\alpha }$ on a concrete realization of the universal covering group of $U(1,1)$. We prove that these functions are, up to a phase factor, radial eigenfunctions of the Landau Hamiltonian on the hyperbolic disc with a magnetic field strength proportional to $\mu $, and corresponding to the eigenvalue $4\alpha ( \alpha -1)$. (English)
Keyword: Flensted-Jensen’s functions
Keyword: universal covering group
Keyword: Landau Hamiltonian
Keyword: hyperbolic disc
MSC: 33C05
MSC: 35J10
MSC: 35Q40
MSC: 43A90
MSC: 57M10
MSC: 58C40
idZBL: Zbl 1164.33301
idMR: MR2305867
DOI: 10.1007/s10492-007-0004-7
Date available: 2009-09-22T18:28:38Z
Last updated: 2020-07-02
Stable URL:
Reference: [1] L. Landau, E.  Lifschitz: Quantum Mechanics: Non-relativistic Theory.Pergamon Press, New York, 1965.
Reference: [2] E. V. Ferapontov, A. P.  Veselov: Integrable Schrödinger operators with magnetic fields: Factorization method on curved surfaces.J.  Math. Phys. 42 (2001), 590–607. MR 1808441, 10.1063/1.1334903
Reference: [3] A. Comtet: On the Landau levels on the hyperbolic plane.Ann. Phys. 173 (1986), 185–209. Zbl 0635.58034, MR 0870891
Reference: [4] J.  Negro, M. A. del Olmo, and A.  Rodriguez-Marco: Landau quantum systems: an approach based on symmetry.J.  Phys.  A, Math. Gen. 35 (2002), 2283–2307. MR 1908725, 10.1088/0305-4470/35/9/317
Reference: [5] M.  Flensted-Jensen: Spherical functions on a simply connected semisimple Lie group.Am.  J.  Math. 99 (1977), 341–361. Zbl 0372.43005, MR 0458063, 10.2307/2373823
Reference: [6] Z.  Mouayn: Characterization of hyperbolic Landau states by coherent state transforms.J.  Phys.  A, Math. Gen. 36 (2003), 8071–8076. Zbl 1058.81037, MR 2007510, 10.1088/0305-4470/36/29/311
Reference: [7] S. A.  Albeverio, P. Exner, and V. A. Geyler: Geometric phase related to point-interaction transport on a magnetic Lobachevsky plane.Lett. Math. Phys. 55 (2001), 9–16. MR 1845795, 10.1023/A:1010943228970
Reference: [8] I. S.  Gradshteyn, I. M. Ryzhik: Table of Integrals, Series and Products.Academic Press, New York-London-Toronto, 1980. MR 0582453
Reference: [9] : Analyse Harmonique (Ecole d’été, d’analyse harmonique, Université de Nancy  I, Septembre  15 au Octobre  3, 1980). Les Cours du C.I.M.P.A..P. Eymard, J. L. Clerc, J. Faraut, M. Raïs, and R. Takahashi (eds.), Centre International de Mathématiques Pures et Appliquées, C.I.M.P.A, 1980. (French)


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