Oscillatory and localized perturbations of periodic structures and the bifurcation of defect modes

Vincent Duchêne, Iva Vukićević, Michael I. Weinstein

Let $Q(x)$ denote a periodic function on the real line. The Schrödinger operator, $H_Q=-{\partial }_x^2+Q(x)$, has $L^2(\mathbb{R})-$ spectrum equal to the union of closed real interv…