Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
- Cite this article as:
- Eliasson, L.H. Commun.Math. Phys. (1992) 146: 447. doi:10.1007/BF02097013
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.