Fisher information in confined hydrogen-like ions

TL;DR

This paper explores how Fisher information varies in confined hydrogen-like ions compared to free atoms, revealing significant differences influenced by quantum numbers, atomic properties, and confinement parameters, with many novel benchmark results.

Contribution

It provides the first detailed systematic analysis of Fisher information in confined hydrogen-like systems, highlighting key differences from free atoms and introducing new benchmark data.

Findings

Fisher information depends on quantum numbers n, l, m in confined systems.

Atomic number and radius significantly influence Fisher information.

New benchmark results for Fisher information in various confinement scenarios.

Abstract

Fisher information (I) is investigated for confined hydrogen atom (CHA)-like systems in conjugate $r$ and $p$ spaces. A comparative study between CHA and free H atom (with respect to $I$) is pursued. In many aspects, inferences in CHA are significantly different from free counterpart; that includes its dependence on $n, l, m$. The role of atomic number and atomic radius is discussed. Further, a detailed systematic result of $I$ with respect to variation of confinement radius $r_c$ is presented, with particular emphasis on \emph{non-zero}-$(l,m)$ states. Several new interesting observations are recorded. Most of these results are of benchmark quality and presented for the first time.