A new coherent states approach to semiclassics which gives Scott's correction

TL;DR

This paper introduces a novel coherent states method to improve semiclassical estimates for Schrödinger operators, providing a new proof of Scott's correction for molecular systems.

Contribution

The paper develops new coherent states and applies them to derive semiclassical estimates, offering a novel proof of Scott's correction in molecular quantum mechanics.

Findings

New coherent states framework for semiclassics

Proof of Scott's correction for molecules

Enhanced semiclassical estimates for Schrödinger operators

Abstract

We introduce new coherent states and use them to prove semi-classical estimates for Schr\"odinger operators with regular potentials. This can be further applied to the Thomas-Fermi potential yielding a new proof of the Scott correction for molecules.