Geodesic
Resonance multiplicity of a perturbed periodic Schrödinger operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 1, pp. 134-145 
Yu. P. Chuburin. Resonance multiplicity of a perturbed periodic Schrödinger operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 1, pp. 134-145. http://geodesic.mathdoc.fr/item/TMF_1998_116_1_a5/
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     author = {Yu. P. Chuburin},
     title = {Resonance multiplicity of a~perturbed periodic {Schr\"odinger} operator},
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     pages = {134--145},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1998_116_1_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the perturbation of a periodic Schrödinger operator by a potential that is periodic in the variables $x_1$ and $x_2$ and exponentially decreases as $|x_3| \to \infty$. Near the zero surface of the derivative of the eigenvalue of the periodic operator in a cell with respect to the third quasi-momentum component, we obtain relations between the resonance multiplicity and the order of the pole of the quantities characterizing the scattering. As a rule, the forward scattering amplitude vanishes on this surface.

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