Properties of R\'enyi complexity ratio of quantum states for central potential

TL;DR

This paper introduces the R'enyi complexity ratio for quantum states, explores its properties, and applies it to various quantum systems and molecules, providing analytical forms and verifying its behavior.

Contribution

It presents the first analytical forms of R'enyi complexity ratio for specific quantum systems and investigates its properties across different potentials and molecules.

Findings

Analytical expressions for R'enyi entropy and complexity ratio are derived.

Properties of R'enyi complexity ratio are verified for several diatomic molecules.

Theorems on the near continuous property of R'enyi complexity ratio are proved.

Abstract

R\'enyi complexity ratio of two density functions is introduced for three and multidimensional quantum systems. Localization property of several density functions are defined and five theorems about near continuous property of R\'enyi complexity ratio are proved by Lebesgue measure. Some properties of R\'enyi complexity ratio are demonstrated and investigated for different quantum systems. Exact analytical forms of R\'enyi entropy, R\'enyi complexity ratio, statistical complexities based on R\'enyi entropy for integral order have been presented for solutions of pseudoharmonic and a family of isospectral potentials. Some properties of R\'enyi complexity ratio are verified for some diatomic molecules (CO, NO, N$_2$, CH, H$_2$, and ScH) and for some other quantum systems.