Entropic measures of Rydberg-like harmonic states

Abstract

The Shannon entropy, the desequilibrium and their generalizations (Rényi and Tsallis entropies) of the three-dimensional single-particle systems in a spherically-symmetric potential $V(r)$ can be decomposed into angular and radial parts. The radial part depends on the analytical form of the potential, but the angular part does not. In this paper we first calculate the angular entropy of any central potential by means of two analytical procedures. Then, we explicitly find the dominant term of the radial entropy for the highly energetic (i.e., Rydberg) stationary states of the oscillator-like systems. The angular and radial contributions to these entropic measures are analytically expressed in terms of the quantum numbers which characterize the corresponding quantum states and, for the radial part, the oscillator strength. In the latter case we use some recent powerful results of the information theory of the Laguerre polynomials and spherical harmonics which control the oscillator-like wavefunctions.

Accepted in International Journal of Quantum Chemistry

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Cited by in corpus (6)

• Rényi and Tsallis entropies of the Aharonov-Bohm ring in uniform magnetic fields
• Analytical Shannon information entropies for all discrete multidimensional hydrogenic states
• Fisher information in confined isotropic harmonic oscillator
• Quantum information measures of the Dirichlet and Neumann hyperspherical dots
• Shannon information entropy for a quantum nonlinear oscillator on a space of non-constant curvature
• Complexity-like properties and parameter asymptotics of ${\mathfrak{L}}_q$-norms of Laguerre and Gegenbauer polynomials