A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces

Abstract : Recently, Carin approximate to ena, [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.
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Article dans une revue
Journal of Mathematical Physics, American Institute of Physics (AIP), 2009, 50 (10), <10.1063/1.3227659>
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Contributeur : Christophe Vignat <>
Soumis le : mercredi 2 mai 2012 - 17:59:15
Dernière modification le : mercredi 2 mai 2012 - 17:59:33

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Christophe Vignat, P. W. Lamberti. A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces. Journal of Mathematical Physics, American Institute of Physics (AIP), 2009, 50 (10), <10.1063/1.3227659>. <hal-00693543>

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