97-520 Fedotov A., Klopp F.

The monodromy matrix for a family of almost periodic Schr\"odinger equations in the adiabatic case. (330K, Uuencoded gzipped Postscript) Sep 24, 97

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Abstract. This work is devoted to the study of a family of almost periodic one-dimensional Schr\"odinger equations. We define a monodromy matrix for this family. We study the asymptotic behavior of this matrix in the adiabatic case. Therefore, we develop a complex WKB method for adiabatic perturbations of periodic Schr\"odinger equations. At last, the study of the monodromy matrix enables us to get some spectral results for the initial family of almost periodic equations.

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