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Flensted-Jensen’s functions attached to the Landau problem on the hyperbolic disc. (English) Zbl 1164.33301
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 $$4\alpha ( \alpha -1)$$.
##### MSC:
 33C05 Classical hypergeometric functions, $${}_2F_1$$ 35J10 Schrödinger operator, Schrödinger equation 35Q40 PDEs in connection with quantum mechanics 43A90 Harmonic analysis and spherical functions
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##### References:
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