Spherical-Symmetry and Spin Effects on the Uncertainty Measures of Multidimensional Quantum Systems with Central Potentials

This work has been done in the framework of the Grant FIS2017-89349P of the Agencia Estatal de Investigacion (Spain)) and the European Regional Development Fund (FEDER), and the Grant FQM-207 of the Agencia de Innovacion y Desarrollo de Andalucia.
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.
Agencia Estatal de Investigacion (Spain) FIS2017-89349P
European Commission FIS2017-89349P
Agencia de Innovacion y Desarrollo de Andalucia FQM-207