Geodesic
Schr\"odinger operator with a perturbed small steplike potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 2, pp. 277-290

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We consider the Schrödinger operator with a potential that is periodic with respect to two variables and has the shape of a small step perturbed by a function decreasing with respect to a third variable. We show that under certain conditions on the magnitudes of the step and the perturbation, a unique level that can be an eigenvalue or a resonance exists near the essential spectrum. We find the asymptotic value of this level. 
@article{TMF_1999_120_2_a7,
     author = {Yu. P. Chuburin},
     title = {Schr\"odinger operator with a perturbed small steplike potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {277--290},
     publisher = {mathdoc},
     volume = {120},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_120_2_a7/}
}
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Yu. P. Chuburin. Schr\"odinger operator with a perturbed small steplike potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 2, pp. 277-290. http://geodesic.mathdoc.fr/item/TMF_1999_120_2_a7/