Orthogonal polynomials and geometry of the quantum harmonic oscillator on constant curvature surfaces

  • Christophe Vignat (Université d'Orsay, Gif sur Yvette, France)
University n.n. Universität Leipzig (Leipzig)


In this talk, starting from results by Carinena et al. [Ann. Phys. 322, 434, 2007] about the quantum harmonic oscillator on constant (positive or negative) curvature surfaces, I will show some properties of the orthogonal polynomials associated with the corresponding wavefunctions. These polynomials have a strong connection with the hyperspherical polynomials, from which they inherit some properties. Moreover, a geometric transformation between the cases of a positive and a negative curvature surface can be made explicit: this transformation can be given an algebraic interpretation in terms of these orthogonal polynomials. Finally, a link can be exhibited with the canonical probability measures involved in the theory of nonextensive statistics.

02.08.10 06.08.10

Information Geometry and its Applications III

Universität Leipzig (Leipzig) University n.n. University n.n.

Antje Vandenberg

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Nihat Ay

Max Planck Institute for Mathematics in the Sciences, Germany

Paolo Gibilisco

Università degli Studi di Roma "Tor Vergata", Italy

František Matúš

Academy of Sciences of the Czech Republic, Czech Republic