薛定谔算子奇异连续谱中没有嵌入特征向量

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-10-30 DOI:10.1007/s13324-024-00948-5

Kota Ujino

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引用次数: 0

摘要

一般来说，具有稀疏势的薛定谔算子具有奇异连续谱，而某个开放区间是纯奇异连续谱。我们给出一个充分条件，使开放区间的端点不是特征值。我们给出了一个半线上具有负稀疏势的薛定谔算子的例子，该算子在任何边界条件下都没有非负的嵌入特征值。

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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No eigenvectors embedded in the singular continuous spectrum of Schrödinger operators

In general a Schrödinger operator with a sparse potential has singular continuous spectrum, and some open interval is purely singular continuous spectrum. We give a sufficient condition so that the endpoint of the open interval is not an eigenvalue. An example of a Schrödinger operator with a negative sparse potential on the half-line which has no nonnegative embedded eigenvalue for any boundary conditions is given.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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