On the bands of the Schrödinger operator with a matrix potential

Oktay Veliev

Mathematische Nachrichten, 2023, vol. 296, issue 3, 1285-1295

Abstract: In this article, we consider the one‐dimensional Schrödinger operator L(Q)$L(Q)$ with a Hermitian periodic m×m$m\times m$ matrix potential Q. We investigate the bands and gaps of the spectrum and prove that most of the positive real axis is overlapped by m bands. Moreover, we find a condition on the potential Q for which the number of gaps in the spectrum of L(Q)$L(Q)$ is finite.

Date: 2023
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https://doi.org/10.1002/mana.202100481

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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:296:y:2023:i:3:p:1285-1295

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