# Shannon entropy: a study of confined hydrogenic-like atoms

## TL;DR

This study investigates Shannon entropy in confined hydrogenic-like atoms, proposing new formulas for entropic uncertainty and analyzing how confinement affects entropy and energy, with results validated against existing data.

## Contribution

Introduces novel expressions for entropic uncertainty and Shannon entropies in confined atoms, and analyzes their behavior across different confinement radii using a variational approach.

## Key findings

- Shannon entropies vary with confinement radius
- New formulas ensure dimensionless and physical consistency
- Results align with previous studies where available

## Abstract

The Shannon entropy in the atomic, molecular and chemical physics context is presented by using as test cases the hydrogenic-like atoms $H_c$, ${He_c}^+$ and ${Li_c}^{2+}$ confined by an impenetrable spherical box. Novel expressions for entropic uncertainty relation and Shannon entropies $S_r$ and $S_p$ are proposed to ensure their physical dimensionless characteristic. The electronic ground state energy and the quantities $S_r$, $S_p$ and $S_t$ are calculated for the hydrogenic-like atoms to different confinement radii by using a variational method. The global behavior of these quantities and different conjectures are analyzed. The results are compared, when available, with those previously published.