A periodic Schrödinger operator with two degenerate spectral gaps (Spectral and Scattering Theory and Related Topics)

Abstract

In this paper, we consider the one-dimensional Schrödinger operators with periodic generalized point interactions. Let us suppose that there are 4 point interactions in the basic period cell (0, 2π). Moreover, we assume that each point interaction is given by a rotation. Under these assumption, we investigate the coexistence problem. Especially, we construct a periodic Schrödinger operators with exactly two degenerate spectral gaps.