New coherent states and a new proof of the Scott correction

TL;DR

The paper introduces new coherent states to establish semi-classical estimates for Schrödinger operators, providing a novel proof of the Scott correction for molecules using these states.

Contribution

It presents a new class of coherent states and applies them to derive semi-classical estimates and a new proof of the Scott correction in molecular quantum mechanics.

Findings

New coherent states for Schrödinger operators

Semi-classical estimates for regular potentials

A new proof of the Scott correction for molecules

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. This is the short version of a paper by the authors archived at math-ph/0208044.