The ionization problem in quantum mechanics

TL;DR

This paper reviews Elliott H. Lieb's contributions to the ionization conjecture in quantum mechanics, which concerns the maximum number of electrons a neutral atom can bind, highlighting progress towards a rigorous proof of this longstanding problem.

Contribution

It summarizes Lieb's foundational work and recent advances related to the ionization conjecture, advancing understanding of electron binding limits in atoms.

Findings

Lieb's work established key bounds on electron numbers in atoms.

Recent developments have made progress towards a rigorous proof of the ionization conjecture.

The review connects historical contributions with current research directions.

Abstract

While it is well-known experimentally that a neutral atom can bind at most one or two extra electrons, deriving this fact rigorously from first principles of quantum mechanics remains a very challenging problem, often referred to as the ionization conjecture. We will review some of Elliott H. Lieb's fundamental contributions to this topic and discuss their impacts on several recent developments.