Quantum information and statistical complexity of hydrogen-like ions in Dunkl-Schr\"odinger system

TL;DR

This paper analytically solves the Dunkl-Schrödinger equation for hydrogen-like ions, exploring eigenvalues, eigenfunctions, and complexity measures, revealing how Dunkl reflection influences quantum properties and complexity in atomic systems.

Contribution

It provides the first analytical expressions for eigenvalues, eigenfunctions, and complexity measures of hydrogen-like ions in a Dunkl reflection framework, expanding understanding of quantum complexity.

Findings

Eigenvalues and eigenfunctions derived for Z=1-3 ions.

Complexity measures vary with Dunkl parameter and parity.

Most results are novel contributions to quantum complexity analysis.

Abstract

In this work, we present analytical solutions of Schr\"odinger equation for Coulomb potential in presence of a Dunkl reflection operator. Expressions are offered for eigenvalues, eigenfunctions and radial densities for H-isoelectronic series (Z=1-3). The degeneracy in energy in absence and presence of the reflection has been discussed. The standard deviation, Shannon entropy, R\'enyi entropy in position space have been derived for arbitrary quantum states. Then several important complexity measures like L\'opez-Ruiz-Mancini-Calbet (LMC), Shape-R\'enyi complexity (SRC), Generalized R\'enyi complexity (GRC), R\'enyi complexity ratio (RCR) are considered in the analytical framework. Representative results are given for three one-electron atomic ions in tabular and graphical format. Changes in these measures with respect to parity and Dunkl parameter have been given in detail. Most of these results are offered here for the first time.