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On the bands of the Schrödinger operator with a matrix potential

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  • Oktay Veliev

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.

Suggested Citation

  • Oktay Veliev, 2023. "On the bands of the Schrödinger operator with a matrix potential," Mathematische Nachrichten, Wiley Blackwell, vol. 296(3), pages 1285-1295, March.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:3:p:1285-1295
    DOI: 10.1002/mana.202100481
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