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Journal of Mathematical Chemistry

Information-theoretic spreading measures of a particle confined in a 3D infinite spherical well

Debraj Nath, Ramon Carbó‐Dorca

Published Mar 5, 2023• 5 citations
Publisher
DOI
10.1007/s10910-023-01460-0

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Abstract The position and momentum spreading of the electron distribution of the two‐dimensional confined hydrogenic atom, which is a basic prototype of the general multidimensional confined quantum systems, is numerically studied in terms of the confinement radius for the 1s, 2s, 2p, and 3d quantum states by means of the main entropy and complexity information‐theoretical measures. First, the Shannon entropy and the Fisher information, as well as the associated uncertainty relations, are computed and discussed. Then, the Fisher‐Shannon, lopezruiz‐mancini‐alvet, and LMC‐Rényi complexity measures are examined and mutually compared. We have found that these entropy and complexity quantities reflect the rich properties of the electron confinement extent in the two conjugated spaces.
Abstract Information‐based uncertainty measures like Rényi entropy (R), Shannon entropy (S) and Onicescu energy (E) are employed to understand the influence of radial confinement in an isotropic harmonic oscillator (IHO). The transformation of the Hamiltonian into a dimensionless form gives an idea of the composite effect of oscillation frequency (ω) and confinement radius (). For a given quantum state, accurate results are provided by applying the respective exact analytical wave function in the r‐space. The p‐space wave functions are produced from Fourier transforms of radial functions. Pilot calculations are done taking order of entropic moments () as in r‐ and p‐spaces. A detailed, systematic analysis is performed for a 3D confined harmonic oscillator (CHO) with respect to state indices , and . It has been found that the CHO acts as a bridge between particles in a spherical box and the 3D free IHO. In the low‐ region, increases while decrease with the rise in . At moderate , there exists an interaction between two competing factors: i) radial confinement (localization) and ii) accumulation of radial nodes with growth of (delocalization). Most of these results are reported here for the first time, revealing many new interesting features.