Universal Monotonicity of Eigenvalue Moments and Sharp Lieb-Thirring Inequalities

TL;DR

This paper demonstrates a universal monotonicity property for eigenvalue moments of Schrödinger operators, leading to a new proof of sharp Lieb-Thirring inequalities, which are fundamental in quantum mechanics.

Contribution

It introduces a novel monotonicity approach to derive universal bounds on eigenvalues, offering a new proof of the sharp Lieb-Thirring inequalities.

Findings

Eigenvalue bounds can be derived from monotonicity properties.

A new proof of sharp Lieb-Thirring inequalities is provided.

Phase space bounds are connected to monotonicity with respect to coupling constants.

Abstract

We show that phase space bounds on the eigenvalues of Schr\"{o}dinger operators can be derived from universal bounds recently obtained by E. M. Harrell and the author via a monotonicity property with respect to coupling constants. In particular, we provide a new proof of sharp Lieb-Thirring inequalities.