A Mathematical Aspect of Hohenberg-Kohn Theorem

TL;DR

This paper explores a mathematical perspective of the Hohenberg-Kohn theorem within density functional theory, focusing on a specific class of external potentials and utilizing a unique continuation principle to deepen understanding.

Contribution

It introduces a mathematical analysis of the Hohenberg-Kohn theorem for certain external potentials using a unique continuation principle, expanding theoretical foundations.

Findings

Established conditions for the theorem's validity with specific potentials

Provided a mathematical proof leveraging unique continuation principles

Enhanced theoretical understanding of density functional theory

Abstract

The Hohenberg-Kohn theorem plays a fundamental role in density functional theory, which has become a basic tool for the study of electronic structure of matter. In this article, we study the Hohenberg-Kohn theorem for a class of external potentials based on a unique continuation principle.