Asymptotic Expansion of the Spectrum for Periodic Schrödinger Operators

.We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schrödinger-type operator with a confining potential and with the principle part of a periodic elliptic operator in divergence form. We compare the spectrum to the homogenized operator and characterize the corrections up to arbitrarily high order.KeywordshomogenizationSchrödingerspectrumMSC codes35J10