The purpose of my talk is devoted to show the existence with accuracy the lower bound of the spectrum corresponding to the Schrödinger operator defined in an open set of a geodesically complete Riemannian manifold, the condition boundary is the Dirichlet. The assumptions on the potential are the average of its positive part is semi-bounded from below, the average operates in a negligible set and regarding the negative part of the potential is bounded in each geodesically cube, i.e. normal cubes.