On the bands of the Schrodinger operator with a matrix potential

Abstract

In this article, we consider the one-dimensional Schrodinger operator L(Q)$L(Q)$ with a Hermitian periodic mxm$m\times m$ 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.