A Mathematical Aspect of Bloch's Theorem

2024/06/26 by Yan Li, Bin Yang, Li, Yan +3
Mathematics · #FOS: Physical sciences #History and Theory of Mathematics #Mathematical Physics (math-ph) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2406.18217

openalex publication_date 2024/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Schrodinger 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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