| 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:
|
http://hdl.handle.net/10338.dmlcz/134665 |
| . |
| 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) |
| . |
