Information theory of quantum systems with some hydrogenic applications

TL;DR

This paper explores the application of information-theoretic measures to quantum systems, especially hydrogenic atoms, to quantify their internal disorder and analyze physical phenomena.

Contribution

It introduces an information-theoretic framework for quantum systems and applies it to hydrogenic models, highlighting its potential for understanding quantum disorder.

Findings

Calculated information measures for hydrogenic systems.

Demonstrated the predictive power of these measures.

Identified open problems in the field.

Abstract

The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the quantum-mechanical non-relativistic systems can be quantified by various single (Fisher information, Shannon entropy) and composite (e.g. Cramer-Rao, LMC shape and Fisher-Shannon complexity) functionals of the Schr\"odinger probability density. First, we examine these concepts and its application to quantum systems with central potentials. Then, we calculate these measures for hydrogenic systems, emphasizing their predictive power for various physical phenomena. Finally, some recent open problems are pointed out.