Various complexity measures in confined hydrogen atom

TL;DR

This paper investigates various statistical complexity measures, including generalized Rényei-based forms, for confined hydrogen atoms in position and momentum spaces, analyzing their behavior with respect to confinement radius and state types.

Contribution

It introduces a comprehensive analysis of multiple complexity measures, including generalized Rényei entropy, for confined hydrogen atoms in both position and momentum spaces, highlighting new patterns and features.

Findings

Complexity measures show maxima and minima for nodal states in position space.

Distinct patterns are absent in momentum space for nodal states.

The study reveals new features of complexity measures with respect to confinement radius.

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 R\'enyi 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.