A Mathematical Aspect of Bloch’s Theorem

IF 2.6 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica Scripta Pub Date : 2024-09-17 DOI:10.1088/1402-4896/ad7767

Yan Li, Bin Yang and Aihui Zhou

引用次数: 0

Abstract

In this paper, by studying a class of 1-D Sturm-Liouville problems with periodic coefficients, we show and classify the solutions of periodic Schrödinger equations in a multidimensional case, which tells that not all the solutions are Bloch solutions. In addition, we also provide several properties of the solutions and quasimomenta and illustrate the relationship between bounded solutions and Bloch solutions.

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布洛赫定理的数学方面

本文通过研究一类具有周期性系数的一维 Sturm-Liouville 问题，展示了周期性薛定谔方程在多维情况下的解并对其进行了分类，告诉人们并非所有的解都是布洛赫解。此外，我们还提供了解和准量子的若干性质，并说明了有界解和布洛赫解之间的关系。

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

Physica Scripta 物理-物理：综合

CiteScore

3.70

自引率

3.40%

发文量

782

审稿时长

4.5 months

期刊介绍： Physica Scripta is an international journal for original research in any branch of experimental and theoretical physics. Articles will be considered in any of the following topics, and interdisciplinary topics involving physics are also welcomed: -Atomic, molecular and optical physics- Plasma physics- Condensed matter physics- Mathematical physics- Astrophysics- High energy physics- Nuclear physics- Nonlinear physics. The journal aims to increase the visibility and accessibility of research to the wider physical sciences community. Articles on topics of broad interest are encouraged and submissions in more specialist fields should endeavour to include reference to the wider context of their research in the introduction.