Dimassi, Mouez Resonances for slowly varying perturbations of a periodic Schrödinger operator. (English) Zbl 1025.81016 Can. J. Math. 54, No. 5, 998-1037 (2002). From the author’s abstract: We study the resonances of the operator \(P(h) = -\Delta_x + V(x) + \varphi(hx)\). Here \(V\) is a periodic potential, \(\varphi\) a decreasing perturbation and \(h\) a small positive constant. We prove the existence of shape resonances near the edges of the spectral bands of \(P_0 = -\Delta_x + V(x)\), and we give its asymptotic expansions in powers of \(h^{\frac 12}\). Reviewer: Ricardo Weder (México City) Cited in 3 Documents MSC: 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory 35Q40 PDEs in connection with quantum mechanics 35B34 Resonance in context of PDEs Keywords:resonances; semi-classical limit PDFBibTeX XMLCite \textit{M. Dimassi}, Can. J. Math. 54, No. 5, 998--1037 (2002; Zbl 1025.81016) Full Text: DOI