Geodesic
On the Sum of Negative Eigenvalues of the Three-Dimensional Schr\"odinger Operator
Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 170-176

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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 $d\geqslant 4$. They also posed the following question: Is the restriction $d\geqslant 4$ 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.
Keywords: sum of negative eigenvalues, Schrödinger operator, Kato potential. 
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     title = {On the {Sum} of {Negative} {Eigenvalues} of the {Three-Dimensional} {Schr\"odinger} {Operator}},
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A. R. Aliev; E. Kh. Eivazov. On the Sum of Negative Eigenvalues of the Three-Dimensional Schr\"odinger Operator. Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 170-176. http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a1/