The Hohenberg-Kohn Theorem for Schrodinger Semigroups

TL;DR

This paper reinterprets the Hohenberg-Kohn theorem within the framework of Schrodinger semigroups, providing a new mathematical perspective on how nuclear potentials are determined by electron densities in quantum systems.

Contribution

It introduces a novel derivation of the Hohenberg-Kohn theorem using the principal eigenvalue of Schrodinger semigroups, bridging quantum chemistry and spectral theory.

Findings

Reformulation of the Hohenberg-Kohn theorem in terms of Schrodinger semigroups

Establishment of a connection between eigenvalues and electron densities

Potential for new mathematical tools in density functional theory

Abstract

At the basis of much of computational chemistry is density functional theory, as initiated by the Hohenberg-Kohn theorem. The theorem states that, when nuclei are fixed, nuclear potentials are determined by $1$-electron densities. We recast and derive this result within the context of the principal eigenvalue of Schrodinger semigroups.