On the Sum of Negative Eigenvalues of the Three-Dimensional Schrödinger Operator

M. Demuth and G. Katriel (arXiv: math.SP/0802.2032) proved the finiteness of the sum of negative eigenvalues of the \(d\) -dimensional Schrödinger operator under certain conditions on the electrical potential for \(d\ge 4\) . They also posed the following question: Is the restriction \(d\ge 4\) a disadvantage of the method, or does it reflect the actual situation? In the present paper, we prove that the technique in the cited paper also works for the three-dimensional Schrödinger operator with Kato potential whose negative part is an integrable function and that this method does not apply to the two-dimensional Schrödinger operator.