Entropic integrals of hyperspherical harmonics and spatial entropy of D-dimensional central potentials

The information entropy of a single particle in a quantum-mechanical D-dime nsional central potential is separated in two parts. One depends only on th e specific form of the potential (radial entropy) and the other depends on the angular distribution (spatial entropy). The latter is given by an entro pic-like integral of the hyperspherical harmonics, which is expressed in te rms of the entropy of the Gegenbauer polynomials. This entropy is expressed in terms of the values of the quadratic logarithmic potential of Gegenbaue r polynomials C-n(lambda)(t) at the zeros of these polynomials. Then this p otential for integer lambda is given as a finite expansion of Chebyshev pol ynomials of even order, whose coefficients are shown to be Wilson polynomia ls. (C) 1999 American Institute of Physics. [S0022- 2488(99)00111-5].