2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171196We show that phase space bounds on the eigenvalues of Schrödinger 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.6 pagesMathematical Physics81Q10, 35P15, 35P20text