Spectral properties of the periodic magnetic Schrödinger operator in the high-energy region. Two-dimensional case

Academic Article


  • The goal is to investigate spectral properties of the operator H = (-i∇ + a(x))2 + a0(x) in the two-dimensional situation, (a(x), a0(x)) being periodic. We construct asymptotic formulae for Bloch eigenvalues and eigenfunctions in the high-energy region, describe properties of isoenergetic curves in the space of quasimomenta and give a new proof of the Bethe-Sommerfeld conjecture. © Springer-Verlag 2004.
  • Digital Object Identifier (doi)

    Author List

  • Karpeshina Y
  • Start Page

  • 473
  • End Page

  • 514
  • Volume

  • 251
  • Issue

  • 3