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arXiv · 1412.6776

A new treatment for some periodic Schrödinger operators I: the eigenvalue

Wei He
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Abstract

We study the problem of how the Floquet property manifests for periodic Schrödinger operators which are known to have multiple of asymptotic spectral solutions. The main conclusions are made for elliptic potentials, we demonstrate that for each period of the elliptic function there is a relation about the Floquet exponent and the monodromy of wave function. Among them there are two relations not explained by the classical Floquet theory. These relations produce both old and new asymptotic solutions consistent with results already known.

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Wei He. 2019-04-05. A new treatment for some periodic Schrödinger operators I: the eigenvalue. https://doi.org/10.1088/0253-6102%2F69%2F2%2F115

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