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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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