This work is devoted to a new version of the complex WKB method suited for adiabatic perturbations of one-dimensional periodic Schrödinger operators. Therefore, we introduce an additional parameter, and it is this parameter (and not the variable of the equation) that will become complex. This naturally leads to canonical domains where we construct solutions of the Schrödinger equation with a standard asymptotic behavior. These can be used to compute the asymptotics of the exponentially small coefficients of transfer matrices (e.g., scattering matrices, monodromy matrices, etc.). We give an example of such a computation.

Original languageEnglish
Pages (from-to)219-264
Number of pages46
JournalAsymptotic Analysis
Volume27
Issue number3-4
StatePublished - 1 Sep 2001

    Research areas

  • Adiabatic perturbations, Complex WKB method, Periodic Schrödinger equation

    Scopus subject areas

  • Mathematics(all)

ID: 35928194