Description
Title: The Ionization Conjecture in Quantum Mechanics and Density Functional Theory: An Introduction
Abstract: Quantum mechanics accurately describes physics on atomic length scales. However, many fundamental questions about the structure of matter remain unanswered. A prominent example is the Ionization Conjecture. It asserts that an atom with nuclear charge Z can bind at most Z+1 electrons. Although this has been experimentally documented since the 1970s, a mathematical proof is not in sight. In this lecture, we introduce the Ionization Conjecture and review some landmark results and recent progress. Although the conjecture for the full many-body problem seems out of reach, significant progress has been made in certain effective single-particle models. These models are easier to study yet still capture key aspects of the full many-body system. Among these are density functional theories such as the classic Thomas–Fermi model, which effectively describe the energy and particle distribution of large atoms and molecules. Remarkably, despite describing the bulk of the electrons, these models also provide insights into the outermost electrons—the key objects in the Ionization Conjecture.
