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Floquet solutions for the Schrödinger equation with fast-oscillating quasi-periodic potentials

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The author is is supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 19KJB110025) and School Foundation of Yangzhou University(Grant No. 2019CXJ009)

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  • In this paper, we study the one-dimensional stationary Schrödinger equation with quasi-periodic potential $ u(\omega t) $. We show that if the frequency vector $ \omega $ is sufficient large, the Schrödinger equation admits two linear independent Floquet solutions for a set of positive measure of energy $ E $. In contrast with previous results, the conditions of small potential $ u $ or large energy $ E $ are no longer needed.

    Mathematics Subject Classification: Primary: 37J40, 34D05.


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