Geodesic
Schr\"odinger Operator Levels for a Crystal Film with a~Nonlocal Potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 2, pp. 297-302

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For a crystal film, we consider the Schrödinger operator defined on Bloch functions (with respect to two variables) in a cell. The potential is the sum of two small terms: a function decreasing with respect to the third variable and an operator of rank one. We prove the existence of two levels (eigenvalues or resonances) near the parameter value $E=0$ and obtain their asymptotic.
Keywords: Schrödinger operator, periodic potential, nonlocal potential, eigenvalue, resonance, asymptotic behavior. 
@article{TMF_2004_140_2_a7,
     author = {M. S. Smetanina and Yu. P. Chuburin},
     title = {Schr\"odinger {Operator} {Levels} for a {Crystal} {Film} with {a~Nonlocal} {Potential}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {297--302},
     publisher = {mathdoc},
     volume = {140},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_140_2_a7/}
}
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M. S. Smetanina; Yu. P. Chuburin. Schr\"odinger Operator Levels for a Crystal Film with a~Nonlocal Potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 2, pp. 297-302. http://geodesic.mathdoc.fr/item/TMF_2004_140_2_a7/