Resonances for Slowly Varying Perturbations of a Periodic Schrödinger Operator

Dimassi, Mouez

Canadian journal of mathematics, Tome 54 (2002) no. 5, pp. 998-1037

Résumé

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 ${{h}^{\frac{1}{2}}}$ .

Détail

DOI : 10.4153/CJM-2002-037-9

Mots-clés : 35P99, 47A60, 47A40

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