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

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-04-22 DOI:10.1134/s0001434624010139

A. R. Aliev, E. H. Eyvazov

引用次数: 0

Abstract

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.

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论三维薛定谔算子的负特征值之和

摘要 M. Demuth 和 G. Katriel（arXiv: math.SP/0802.2032）证明了在\(d\ge 4\) 电势的某些条件下，\(d\)维薛定谔算子负特征值之和的有限性。他们还提出了以下问题：限制 \(d\ge 4\) 是该方法的缺点，还是它反映了实际情况？在本文中，我们证明了引用论文中的技术也适用于负部分为可积分函数的具有加藤电势的三维薛定谔算子，而这种方法不适用于二维薛定谔算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.