Communications in Mathematical Physics

, Volume 146, Issue 3, pp 447–482

Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation

  • L. H. Eliasson
Article

DOI: 10.1007/BF02097013

Cite this article as:
Eliasson, L.H. Commun.Math. Phys. (1992) 146: 447. doi:10.1007/BF02097013

Abstract

We show that the 1-dimensional Schrödinger equation with a quasiperiodic potential which is analytic on its hull admits a Floquet representation for almost every energyE in the upper part of the spectrum. We prove that the upper part of the spectrum is purely absolutely continuous and that, for a generic potential, it is a Cantor set. We also show that for a small potential these results extend to the whole spectrum.

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • L. H. Eliasson
    • 1
  1. 1.Department of MathematicsRoyal Institute of TechnologyStockholmSweden

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