2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146166The main purpose of this paper is to show that the generalized Schrödinger operator ${\cal A}^Vf={1/2}Δf+b\nabla f-Vf$, $f\in C_0^\infty(\R^d)$, is a pre-generator for which we can prove its $L^\infty(\R^d,dx)$-uniqueness. Moreover, we prove the $L^1(\R^d,dx)$-uniqueness of weak solutions for the Fokker-Planck equation associated with this pre-generator.Mathematical PhysicsPrimary: 47D03, 47F05. Secondary: 60J60text