Various complexity measures in confined hydrogen atom

Abstract

Several well-known statistical measures similar to \emph{LMC} and \emph{Fisher-Shannon} complexity have been computed for confined hydrogen atom in both position ($r$) and momentum ($p$) spaces. Further, a more generalized form of these quantities with Rényi entropy ($R$) is explored here. The role of scaling parameter in the exponential part is also pursued. $R$ is evaluated taking order of entropic moments $\alpha ,\beta$ as $(\frac{2}{3},3)$ in $r$ and $p$ spaces. Detailed systematic results of these measures with respect to variation of confinement radius $r_c$ is presented for low-lying states such as, $1s$-$3d,4f$ and $5g$. For \emph{nodal} states, such as $2s,3s$ and $3p$, as $r_c$ progresses there appears a maximum followed by a minimum in $r$ space, having certain values of the scaling parameter. However, the corresponding $p$-space results lack such distinct patterns. This study reveals many other interesting features.

15 pages, 4 tables, 4 figures

References in corpus (2)

• Information Entropy, Information Distances and Complexity in Atoms
• Statistical complexity, Fisher-Shannon information, and Bohr orbits in the H-atom

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