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# Resonances for Slowly Varying Perturbations of a Periodic Schrödinger Operator

Published:2002-10-01
Printed: Oct 2002
• Mouez Dimassi
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## 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 $h^{\frac12}$.
 MSC Classifications: 35P99 - None of the above, but in this section 47A60 - Functional calculus 47A40 - Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]

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