Coulomb Correlation and Information Entropies in Confined Helium-Like Atoms

The present work studies aspects of the electronic correlation in confined H$^{-}$, He and Li$^+$ atoms in their ground states using the informational entropies. In this way, different variational wavefunctions are employed in order of better take account of Coulomb correlation. The obtained values for the $S_r$, $S_p$ and $S_t$ entropies are sensitive in relation to Coulomb correlation effects. In the strong confinement regime, the effects of the Coulomb correlation are negligible and the employment of the models of independent particle and two non-interacting electrons confined by a impenetrable spherical cage gains importance in this regime. Lastly, energy values are obtained in good agreement with the results available in the literature.Comment: Version accepted for publication in European Physical Journal

Electron Confinement study in a double quantum dot by means of Shannon Entropy Information

In this work, we use the Shannon informational entropies to study an electron confined in a double quantum dot; we mean the entropy in the space of positions, $S_r$, in the space of momentum, $S_p$, and the total entropy, $S_t = S_r+S_p$. We obtain $S_r$, $S_p$ and $S_t$ as a function of the parameters $A_2$ and $k$ which rules the height and the width, respectively, of the internal barrier of the confinement potential. We conjecture that the entropy $S_r$ maps the degeneracy of states when we vary $A_2$ and also is an indicator of the level of decoupling/coupling of the double quantum dot. We study the quantities $S_r$ and $S_p$ as measures of delocalization/localization of the probability distribution. Furthermore, we analyze the behaviors of the quantities $S_p$ and $S_t$ as a function of $A_2$ and $k$. Finally, we carried out an energy analysis and, when possible, compared our results with work published in the literature.Comment: Version accepted for publication in Physica B: Condensed Matte

STUDY OF SHANNON ENTROPY IN THE CONTEXT OF QUANTUM MECHANICS: AN APPLICATION TO FREE AND CONFINED HARMONIC OSCILLATOR

The aim of this study was a didactic presentation of the Shannon entropy in the quantum theory context, followed by application to the case of a one-dimensional harmonic oscillator in its ground state, both in the free case and confined case. The study of these systems allows us to highlight notions such as location or delocation of a particle, a possible interpretation that the Shannon entropy can adopt. The Shannon entropy in position (Sx) and momentum (Sp) spaces were calculated for both systems, beyond the entropic sum (St = Sx + Sp). With this procedure it was possible to identify trends in the behavior of the Shannon entropy (Sx and Sp) and test the compliance of the entropic uncertainty relation (St = Sx + Sp ≥ n(1 + ln(π)))

A Study of Strong Confinement Regions Using Informational Entropy

We present an informational study of a spherically confined hydrogen atom, a hydrogenic ion confined in a strongly coupled plasma, a spherically confined harmonic oscillator, and a particle confined in a cage. For this, we have implemented a numerical procedure to obtain information entropies of these confined quantum systems. The procedure is based on the variational formalism that uses the finite element method (FEM) for the expansion of the wavefunction in terms of local base functions. Such a study is carried out in order to analyze what happens in the rigorous confinement regime. In particular, we have shown that the effects of the interaction potential is no longer important for rigorous confinements and the studied systems start to behave just like an electron confined by a impenetrable spherical cage. When possible, we compared our results with those published in the literature