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Flensted-Jensen’s functions; universal covering group; Landau Hamiltonian; hyperbolic disc
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 $4\alpha ( \alpha -1)$.
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