2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/198922We give a proof of the Lieb-Thirring inequality in the critical case $d=1$, $γ= 1/2$, which yields the best possible constant.Revised version. 14 pages, Latex2e, no figures. Some typos on p.3 corrected and journal ref addedMathematical PhysicsA sharp bound for an eigenvalue moment of the one-dimensional Schroedinger operatortext