%0 Journal Article
%T On the eigenvalues for slowly varying perturbations of a periodic Schr£żdinger operator
%A Magali Marx
%J Mathematics
%D 2005
%I arXiv
%X In this paper, I consider one-dimensional periodic Schr{\"o}dinger operators perturbed by a slowly decaying potential. In the adiabatic limit, I give an asymptotic expansion of the eigenvalues in the gaps of the periodic operator. When one slides the perturbation along the periodic potential, these eigenvalues oscillate. I compute the exponentially small amplitude of the oscillations.
%U http://arxiv.org/abs/math-ph/0503031v1