2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164034We prove conditions on potentials which imply that the sum of the negative eigenvalues of the Schroeodinger operator is finite. We use a method for bounding eigenvalues based on estimates of the Hilbert-Schmidt norm of semigroup differences and on complex analysisSpectral TheoryMathematical Physics35J10; 35P15; 81Q10On finiteness of the sum of negative eigenvalues of Schroedinger operatorstext