POSITION AND MOMENTUM INFORMATION ENTROPIES OF THE D-DIMENSIONAL HARMONIC-OSCILLATOR AND HYDROGEN-ATOM

The position- and momentum-space entropies of the isotropic harmonic o scillator and the hydrogen atom in D dimensions are shown to be relate d to some entropy integrals which involve classical orthogonal polynom ials. These integrals are exactly calculated for Chebyshev polynomials and only in an approximate way for Gegenbauer polynomials. The physic al entropies are explicitly obtained in the ground state and in a few low-lying excited states. Finally, the dimensionality dependence of th e ground-state entropies of the two above-mentioned quantum-mechanical systems is analyzed (numerically) and the values of the entropies in a large class of excited states of the D-dimensional (D = 1, 2,3) harm onic oscillator and hydrogen atom are tabulated and discussed.