薛定谔算子与谱守恒律的eigenvalue和的下界
Lower bounds on the eigenvalue sums of the Schrödinger operator and the spectral conservation law
摘要：
本文第一部分考虑Schr dinger算子$ -Δ-V(x),\quad V>0. $，讨论了$V$在无穷远处的行为与$H$的负谱性质之间的关系。在此之后，我们考虑当$V$改变其符号时的情况：$ V=V_+-V_-$，$2V_\pm=|V|\pm V. $在这种情况下，我们对称地处理$V$和$-V$，并研究$V$在无穷远处的行为与算子$H_+=-Δ+V$和$H_-=-Δ-V$的负谱之间的关系。
英文摘要：
In the first part of the paper we consider the Schrödinger operator $ -Δ-V(x),\quad V>0. $ We discuss the relation between the behavior of $V$ at the infinity and the properties of the negative spectrum of $H$. After that, we consider the case when $V$ changes its sign: $ V=V_+-V_-$, $2V_\pm=|V|\pm V. $ In this case, we treat $V$ and $-V$ symmetrically and study the relation between the behavior of $V$ at the infinity and the negative spectra of the operators $H_+=-Δ+V$ and $H_-=-Δ-V$.
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