2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70943We give a new lower bound for the first gap $λ_2 - λ_1$ of the Dirichlet eigenvalues of the Schr{ö}dinger operator on a bounded convex domain $Ω$ in R$^n$ or S$^n$ and greatly sharpens the previous estimates. The new bound is explicit and computable.enhanced results, 26 pagesDifferential GeometryMathematical PhysicsAnalysis of PDEsPrimary 35J10; Secondary 35P15, 53C21text