Lower bounds on the eigenvalue sums of the Schrödinger operator and the spectral conservation law

Oleg Safronov

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arXiv · 1002.0080

Lower bounds on the eigenvalue sums of the Schrödinger operator and the spectral conservation law

Oleg Safronov

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Abstract

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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BibTeX RIS

Oleg Safronov. 2010-02-12. Lower bounds on the eigenvalue sums of the Schrödinger operator and the spectral conservation law. https://arxiv.org/abs/1002.0080

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