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Communications in Mathematical Physics

, Volume 146, Issue 3, pp 447–482 | Cite as

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

  • L. H. Eliasson
Article

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.

Keywords

Neural Network Statistical Physic Complex System Hull Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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