A Mathematical Aspect of Bloch's Theorem
Mathematical Physics
2024-06-27 v1 math.MP
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.
Keywords
Cite
@article{arxiv.2406.18217,
title = {A Mathematical Aspect of Bloch's Theorem},
author = {Yan Li and Bin Yang and Aihui Zhou},
journal= {arXiv preprint arXiv:2406.18217},
year = {2024}
}