2014/12/31 by Wei He
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Eigenvalues and eigenvectors #Elliptic function #Elliptic operator #Exponent #Floquet theory #Function (biology) #Mathematical analysis #Mathematical physics #Mathematics #Monodromy #Monodromy matrix #Nonlinear system #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Schrödinger's cat #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.MP #math.SP #msc:33E10 #msc:34E10 #msc:35P20
paper · pdf · doi:10.1088/0253-6102/69/2/115
published as Commun. Theor. Phys. 69 (2018) 115-126 · 24 pages; journal version
openalex publication_date 2018/02/01 · openalex created_date 2018/03/29 · arxiv created 2019/04/05 · arxiv updated 2019/05/28 · openalex updated_date 2026/08/05
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 Floquwet theory. These relations produce both old and new asymptotic solutions consistent with results already known.