New bounds on the Lieb-Thirring constants

TL;DR

This paper improves the bounds on Lieb-Thirring constants for eigenvalue moments of Schrödinger operators within a specific parameter range, enhancing theoretical understanding of spectral inequalities.

Contribution

It provides new, tighter bounds on Lieb-Thirring constants for certain eigenvalue moment inequalities, advancing mathematical spectral theory.

Findings

Derived improved bounds for $L_{ ext{γ,d}}$ constants

Extended the range of γ for which bounds are known

Enhanced understanding of eigenvalue inequalities in quantum mechanics

Abstract

Improved estimates on the constants $L_{\gamma,d}$, for $1/2<\gamma<3/2$, $d\in N$ in the inequalities for the eigenvalue moments of Schr\"{o}dinger operators are established.