Information theory of quantum systems with some hydrogenic applications

The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the quantum-mechanical non-relativistic systems can be quantified by various single (Fisher information, Shannon entropy) and composite (e.g. Cramer-Rao, LMC shape and Fisher-Shannon complexity) functionals of the Schr\"odinger probability density. First, we examine these concepts and its application to quantum systems with central potentials. Then, we calculate these measures for hydrogenic systems, emphasizing their predictive power for various physical phenomena. Finally, some recent open problems are pointed out.Comment: 9 pages, 3 figure

Quantum Entanglement in (d−1)(d-1)-Spherium

There are very few systems of interacting particles (with continuous variables) for which the entanglement of the concomitant eigenfunctions can be computed in an exact, analytical way. Here we present analytical calculations of the amount of entanglement exhibited by $s$-states of \emph{spherium}. This is a system of two particles (electrons) interacting via a Coulomb potential and confined to a $(d-1)$-sphere (that is, to the surface of a $d$-dimensional ball). We investigate the dependence of entanglement on the radius $R$ of the system, on the spatial dimensionality $d$, and on energy. We find that entanglement increases monotonically with $R$, decreases with $d$, and also tends to increase with the energy of the eigenstates. These trends are discussed and compared with those observed in other two-electron atomic-like models where entanglement has been investigated.Comment: 14 pages, 6 figures. J. Phys. A (2015). Accepte