{"title":"布洛赫定理的数学方面","authors":"Yan Li, Bin Yang and Aihui Zhou","doi":"10.1088/1402-4896/ad7767","DOIUrl":null,"url":null,"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.","PeriodicalId":20067,"journal":{"name":"Physica Scripta","volume":"39 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Mathematical Aspect of Bloch’s Theorem\",\"authors\":\"Yan Li, Bin Yang and Aihui Zhou\",\"doi\":\"10.1088/1402-4896/ad7767\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":20067,\"journal\":{\"name\":\"Physica Scripta\",\"volume\":\"39 1\",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physica Scripta\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1402-4896/ad7767\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica Scripta","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1402-4896/ad7767","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
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.
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.
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