Korean J. Math. Vol. 26 No. 4 (2018) pp.601-614
DOI: https://doi.org/10.11568/kjm.2018.26.4.601

Absolute continuity of the magnetic Schrodinger operator with periodic potential

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Published: Dec 30, 2018
Keywords:
Schr\"odinger operator, periodic potential, harmonic oscillator, continuous spectrum, Floquet theory, open gaps
Mathematics Subject Classification:
35P05, 35J10, 34L05, 81Q10

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Assel Rachid
Department of Mathematics University of Monastir, Tunisia

Abstract

We consider the magnetic Schr\"odinger operator coupled with two different potentials. One of them is a harmonic oscillator and the other is a periodic potential. We give some periodic potential classes for which the operator has purely absolutely continuous spectrum. We also prove that for strong magnetic field or large coupling constant, there are open gaps in the spectrum and we give a lower bound on their number.


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