Article
MSC:
33C05,
35J10,
35Q40,
43A90,
57M10,
58C40 | MR 2305867 | Zbl 1164.33301 | DOI: 10.1007/s10492-007-0004-7
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Keywords:
Flensted-Jensen’s functions; universal covering group; Landau Hamiltonian; hyperbolic disc
Flensted-Jensen’s functions; universal covering group; Landau Hamiltonian; hyperbolic disc
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 $4\alpha ( \alpha -1)$.
References:
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