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Zbl 1025.81016
Dimassi, Mouez
Resonances for slowly varying perturbations of a periodic Schrödinger operator.
(English)
[J] Can. J. Math. 54, No.5, 998-1037 (2002). ISSN 0008-414X; ISSN 1496-4279/e

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 $h^{\frac 12}$.
[Ricardo Weder (México City)]
MSC 2000:
*81Q20 Semi-classical techniques in quantum theory
35Q40 PDE from quantum mechanics
35B34 Resonances

Keywords: resonances; semi-classical limit

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