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

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    * Corresponding author

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.

    Citation:

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