# Some complexity measures in confined isotropic harmonic oscillator

## TL;DR

This paper investigates various statistical complexity measures, including generalized Rényi-based forms, for the confined isotropic harmonic oscillator across different energy states and confinement radii, revealing new insights into their behavior.

## Contribution

It introduces a generalized form of complexity measures using Rényi entropy for CHO and systematically analyzes their variation with confinement parameters and energy states.

## Key findings

- New features of complexity measures with Rényi entropy are reported.
- Explicit dependence of measures on confinement radius is provided.
- Analysis covers multiple energy states revealing unreported behaviors.

## Abstract

Various well-known statistical measures like \emph{L\'opez-Ruiz, Mancini, Calbet} (LMC) and \emph{Fisher-Shannon} complexity have been explored for confined isotropic harmonic oscillator (CHO) in composite position ($r$) and momentum ($p$) spaces. To get a deeper insight about CHO, a more generalized form of these quantities with R\'enyi entropy ($R$) is invoked here. The importance of scaling parameter in the exponential part is also investigated. $R$ is estimated considering order of entropic moments $\alpha, \beta$ as $(\frac{2}{3},3)$ in $r$ and $p$ spaces respectively. Explicit results of these measures with respect to variation of confinement radius $r_c$ is provided systematically for first eight energy states, namely, $1s,~1p,~1d,~2s,~1f,~2p,~1g$ and $2d$. Detailed analysis of these complexity measures provides many hitherto unreported interesting features.