On the Bands of the Schrodinger Operator with a Matrix Potential

O. A. Veliev

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arXiv · 2109.00999

On the Bands of the Schrodinger Operator with a Matrix Potential

O. A. Veliev

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Abstract

In this article we consider the one-dimensional Schrodinger operator L(Q) with a Hermitian periodic m by m matrix potential Q. We investigate the bands and gaps of the spectrum and prove that the main part 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) is finite.

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O. A. Veliev. 2021-09-02. On the Bands of the Schrodinger Operator with a Matrix Potential. https://arxiv.org/abs/2109.00999

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