On the schrödinger operator with limit-periodic potential in dimension two

Academic Article

Abstract

  • This is an an nouncement of the following results. We consider the Schrödinger operator H=−Δ+V(x) in dimension two, V(x) being a limitperiodic potential. We prove that the spectrum of H contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves e (k,x)at the high energy region. Second, the isoenergetic curves in the space of momenta kk corresponding to these eigenfunctions have a form of slightly distorted circles with holes (Cantor type structure). Third, the spectrum corresponding to the eigenfunctions (the semiaxis) is absolutely continuous. i
  • Digital Object Identifier (doi)

    Author List

  • Karpeshina Y; Lee YR
  • Start Page

  • 257
  • End Page

  • 265
  • Volume

  • 186