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

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.

24 pages; journal version

References in corpus (1)

• Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations

Cited by in corpus (4)

• Oscillatory states of quantum Kapitza pendulum
• A new treatment for some periodic Schrödinger operators II: the wave function
• Spectra of elliptic potentials and supersymmetric gauge theories
• Properties of some elliptic Hill's potentials