English

On the Bands of the Schrodinger Operator with a Matrix Potential

Spectral Theory 2022-06-22 v2 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2109.00999,
  title  = {On the Bands of the Schrodinger Operator with a Matrix Potential},
  author = {O. A. Veliev},
  journal= {arXiv preprint arXiv:2109.00999},
  year   = {2022}
}