Sharp asymptotics of the quasimomentum

Article type: Research Article

Authors: Korotyaev, Evgeny L.

Affiliations: Mathematical Physics Department, Faculty of Physics, Ulianovskaya 2, St. Petersburg State University, St. Petersburg, 198904 Russia and Pushkin Leningrad State University, Russia. E-mail: [email protected]

Abstract: We consider the Schrödinger operator with a periodic potential p on the real line. We assume that p belongs to the real Sobolev space Hm on the circle for some m≥−1. We determine the sharp asymptotics of the quasimomentum and the Titchmarsh–Weyl functions, the Bloch functions at high energy.

Keywords: quasimomentum, integrated density of states, periodic potential

DOI: 10.3233/ASY-2012-1115

Journal: Asymptotic Analysis, vol. 80, no. 3-4, pp. 269-287, 2012