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Flensted-Jensen's functions attached to the Landau problem on the hyperbolic disc

Zouhaïr Mouayn (2007)

Applications of Mathematics

We give an explicit expression of a two-parameter family of Flensted-Jensen’s functions Ψ μ , α 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 μ , and corresponding to the eigenvalue 4 α ( α - 1 ) .

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