Geodesic
Resonance multiplicity of a~perturbed periodic Schr\"odinger operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 1, pp. 134-145

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. 
@article{TMF_1998_116_1_a5,
     author = {Yu. P. Chuburin},
     title = {Resonance multiplicity of a~perturbed periodic {Schr\"odinger} operator},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {134--145},
     publisher = {mathdoc},
     volume = {116},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_116_1_a5/}
}
TY  - JOUR
AU  - Yu. P. Chuburin
TI  - Resonance multiplicity of a~perturbed periodic Schr\"odinger operator
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1998
SP  - 134
EP  - 145
VL  - 116
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1998_116_1_a5/
LA  - ru
ID  - TMF_1998_116_1_a5
ER  - 
%0 Journal Article
%A Yu. P. Chuburin
%T Resonance multiplicity of a~perturbed periodic Schr\"odinger operator
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1998
%P 134-145
%V 116
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1998_116_1_a5/
%G ru
%F TMF_1998_116_1_a5
Yu. P. Chuburin. Resonance multiplicity of a~perturbed periodic Schr\"odinger operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 1, pp. 134-145. http://geodesic.mathdoc.fr/item/TMF_1998_116_1_a5/