# One-parameter Fisher-R\'enyi complexity: Notion and hydrogenic applications

## TL;DR

This paper introduces a one-parameter Fisher-Rényi complexity measure for multidimensional probability distributions and applies it analytically to hydrogenic quantum systems, linking it to quantum numbers and nuclear charge.

## Contribution

It defines and analyzes a new complexity measure and derives its explicit form for hydrogenic systems based on quantum parameters.

## Key findings

- Analytic expression for the complexity measure in hydrogenic systems
- Connection between complexity and quantum numbers
- Insights into the structure of quantum states through complexity

## Abstract

In this work the one-parameter Fisher-R\'enyi measure of complexity for general $d$-dimensional probability distributions is introduced and its main analytic properties are discussed. Then, this quantity is determined for the hydrogenic systems in terms of the quantum numbers of the quantum states and the nuclear charge.