Sharp asymptotics of the quasimomentum

Abstract

We consider the Schrödinger operator with a periodic potential $p$ on the real line. We assume that $p$ belongs to the Sobolev space $\mH_m$ on the circle for some $m\ge -1$, and we determine the asymptotics of the quasimomentum and the Titchmarsh-Weyl functions, the Bloch functions at high energy.

16 pages, 3 figures, keywords: quasimomentum, integrated density of states, periodic potential

References in corpus (1)

• Nonlinear Propagation of Light in One Dimensional Periodic Structures