Spherical-Symmetry and Spin Effects on the Uncertainty Measures of Multidimensional Quantum Systems with Central Potentials
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MDPI
Materia
Central potentials Uncertainty relations Integral inequalities Heisenberg-like uncertainty measures Entropy-like measures Fisher information Shannon entropy Rényi entropies
Date
2021-05-14Referencia bibliográfica
Dehesa, J.S. Spherical-Symmetry and Spin Effects on the Uncertainty Measures of Multidimensional Quantum Systems with Central Potentials. Entropy 2021, 23, 607. [https://doi.org/10.3390/e23050607]
Sponsorship
Agencia Estatal de Investigacion (Spain) FIS2017-89349P; European Commission FIS2017-89349P; Agencia de Innovacion y Desarrollo de Andalucia FQM-207Abstract
The spreading of the stationary states of the multidimensional single-particle systems with a central potential is quantified by means of Heisenberg-like measures (radial and logarithmic expectation values) and entropy-like quantities (Fisher, Shannon, Renyi) of position and momentum probability densities. Since the potential is assumed to be analytically unknown, these dispersion and information-theoretical measures are given by means of inequality-type relations which are explicitly shown to depend on dimensionality and state's angular hyperquantum numbers. The spherical-symmetry and spin effects on these spreading properties are obtained by use of various integral inequalities (Daubechies-Thakkar, Lieb-Thirring, Redheffer-Weyl, ...) and a variational approach based on the extremization of entropy-like measures. Emphasis is placed on the uncertainty relations, upon which the essential reason of the probabilistic theory of quantum systems relies.