2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171875We prove $-Δ+V$ has purely discrete spectrum if $V\geq 0$ and, for all $M$, $|\{x\mid V(x)<M\}|<\infty$ and various extensions.Spectral Theory47B07, 35Q40, 47N50text