Geodesic
On small perturbations of the Schrödinger equation with periodic potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 3, pp. 443-453 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider small perturbations of the potential periodic in variables $x_j$, $j=1,2,3$, by a function wich is periodic in $x_1$, $x_2$ and exponentially decreases as $|x_3|\to\infty$. We prove that close to energies corresponding to the extrema in the third component of the quasy-momentum of nondegenerate eigenvalues of the Schrödinger operator with periodic potential considered in the cell there exists a unique (up to multiplicative factor) solution of the integral equation describing both eigenvalues and resonance levels. The asymptotic behaviour of the latter quantities is described. 
@article{TMF_1997_110_3_a7,
     author = {Yu. P. Chuburin},
     title = {On small perturbations of the {Schr\"odinger} equation with periodic potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {443--453},
     year = {1997},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1997_110_3_a7/}
}
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Yu. P. Chuburin. On small perturbations of the Schrödinger equation with periodic potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 3, pp. 443-453. http://geodesic.mathdoc.fr/item/TMF_1997_110_3_a7/

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