Geodesic
Flensted-Jensen's functions attached to the Landau problem on the hyperbolic disc
Applications of Mathematics, Tome 52 (2007) no. 2, pp. 97-104

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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 $4\alpha ( \alpha -1)$.
DOI : 10.1007/s10492-007-0004-7
Classification : 33C05, 35J10, 35Q40, 43A90, 57M10, 58C40
Keywords: Flensted-Jensen’s functions; universal covering group; Landau Hamiltonian; hyperbolic disc 
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     title = {Flensted-Jensen's functions attached to the {Landau} problem on the hyperbolic disc},
     journal = {Applications of Mathematics},
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Mouayn, Zouhaïr. Flensted-Jensen's functions attached to the Landau problem on the hyperbolic disc. Applications of Mathematics, Tome 52 (2007) no. 2, pp. 97-104. doi: 10.1007/s10492-007-0004-7

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