Asymptotic expansion of the spectrum for periodic Schrödinger operators

Abstract

We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schrödinger-type operator with a confining potential and with principle part a periodic elliptic operator in divergence form. We compare the spectrum to the homogenized operator and characterize the corrections up to arbitrarily high order.

arXiv comment34 pages, to appear in SIAM J. Math. Anal