Conference abstracts

Session C7 - Special Functions and Orthogonal Polynomials

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Entropic functionals of Laguerre and Gegenbauer polynomials with large parameters

David Puertas Centeno

Universidad de Granada, España   -   vidda@correo.ugr.es

The determination of the physical entropies (Rényi, Shannon, Tsallis) of high-dimensional quantum systems subject to a central potential requires the knowledge of the asymptotics of some power and logarithmic integral functionals of the hypergeometric orthogonal polynomials which control the wavefunctions of the stationary states. For the D-dimensional hydrogenic and oscillator-like systems, the wavefunctions of the corresponding bound states are controlled by the Laguerre $(\mathcal L^{(\alpha)}_m(x))$ and Gegenbauer $(\mathcal C^{(\alpha)}_m (x))$ polynomials in both position and momentum spaces, where the parameter $\alpha$ linearly depends on D. In this work we study the asymptotic behavior as $\alpha\to\infty$ of the associated entropy-like integral functionals of these two families of hypergeometric polynomials. Finally, further extension of these results are applied to hyperspherical harmonics together with some quantum applications.

Joint work with Nico M. Temme (IAA, Netherlands), Irene V. Toranzo (Universidad de Granada, Spain) and Jesús S. Dehesa (Universidad de Granada, Spain).

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