102 research outputs found
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 -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 -states of \emph{spherium}. This
is a system of two particles (electrons) interacting via a Coulomb potential
and confined to a -sphere (that is, to the surface of a -dimensional
ball). We investigate the dependence of entanglement on the radius of the
system, on the spatial dimensionality , and on energy. We find that
entanglement increases monotonically with , decreases with , 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
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