Geodesic
Quasilevels of a two-particle Schrödinger operator with a perturbed periodic potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 1, pp. 115-125
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We consider a two-dimensional periodic Schrödinger operator perturbed by the interaction potential of two one-dimensional particles. We prove that quasilevels (i.e., eigenvalues or resonances) of the given operator exist for a fixed quasimomentum and a small perturbation near the band boundaries of the corresponding periodic operator. We study the asymptotic behavior of the quasilevels as the coupling constant goes to zero. We obtain a simple condition for a quasilevel to be an eigenvalue.
Keywords: two-particle Schrödinger operator, periodic potential, eigenvalue, resonance. 
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     author = {Yu. P. Chuburin},
     title = {Quasilevels of a~two-particle {Schr\"odinger} operator with a~perturbed periodic potential},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_158_1_a6/}
}
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Yu. P. Chuburin. Quasilevels of a two-particle Schrödinger operator with a perturbed periodic potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 1, pp. 115-125. http://geodesic.mathdoc.fr/item/TMF_2009_158_1_a6/

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