On the Sum of Negative Eigenvalues of the Three-Dimensional Schr\"odinger Operator

A. R. Aliev ; E. Kh. Eivazov

Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 170-176.

Résumé

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.

Détail

Keywords: sum of negative eigenvalues, Schrödinger operator, Kato potential.

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