Defect Modes and Homogenization of Periodic Schrödinger Operators

Abstract

DEFECT MODES AND HOMOGENIZATION OF PERIODIC SCHRÖDINGER OPERATORS∗ M. A. HOEFER† AND M. I. WEINSTEIN‡ Abstract. We consider the discrete eigenvalues of the operator Hε = −Δ + V (x) + ε2Q(εx), where V (x) is periodic and Q(y) is localized on Rd, d ≥ 1. For ε > 0 and sufficiently small, discrete eigenvalues may bifurcate (emerge) from spectral band edges of… (More)
DOI: 10.1137/100807302

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Cite this paper

@article{Hoefer2011DefectMA, title={Defect Modes and Homogenization of Periodic Schr{\"{o}dinger Operators}, author={Mark Hoefer and Michael I. Weinstein}, journal={SIAM J. Math. Analysis}, year={2011}, volume={43}, pages={971-996} }