Position and momentum information entropies of the D-dimensional harmonic oscillator and hydrogen atom
Physical Review A, 1994•APS
The position-and momentum-space entropies of the isotropic harmonic oscillator and the
hydrogen atom in D dimensions are shown to be related to some entropy integrals which
involve classical orthogonal polynomials. These integrals are exactly calculated for
Chebyshev polynomials and only in an approximate way for Gegenbauer polynomials. The
physical entropies are explicitly obtained in the ground state and in a few low-lying excited
states. Finally, the dimensionality dependence of the ground-state entropies of the two …
hydrogen atom in D dimensions are shown to be related to some entropy integrals which
involve classical orthogonal polynomials. These integrals are exactly calculated for
Chebyshev polynomials and only in an approximate way for Gegenbauer polynomials. The
physical entropies are explicitly obtained in the ground state and in a few low-lying excited
states. Finally, the dimensionality dependence of the ground-state entropies of the two …
Abstract
The position-and momentum-space entropies of the isotropic harmonic oscillator and the hydrogen atom in D dimensions are shown to be related to some entropy integrals which involve classical orthogonal polynomials. These integrals are exactly calculated for Chebyshev polynomials and only in an approximate way for Gegenbauer polynomials. The physical entropies are explicitly obtained in the ground state and in a few low-lying excited states. Finally, the dimensionality dependence of the 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) harmonic oscillator and hydrogen atom are tabulated and discussed.
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