Geodesic
Schrödinger Operator Levels for a Crystal Film with a Nonlocal Potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 2, pp. 297-302 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2004},
     volume = {140},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_140_2_a7/}
}
TY  - JOUR
AU  - M. S. Smetanina
AU  - Yu. P. Chuburin
TI  - Schrödinger Operator Levels for a Crystal Film with a Nonlocal Potential
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2004
SP  - 297
EP  - 302
VL  - 140
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2004_140_2_a7/
LA  - ru
ID  - TMF_2004_140_2_a7
ER  - 
%0 Journal Article
%A M. S. Smetanina
%A Yu. P. Chuburin
%T Schrödinger Operator Levels for a Crystal Film with a Nonlocal Potential
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2004
%P 297-302
%V 140
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2004_140_2_a7/
%G ru
%F TMF_2004_140_2_a7
M. S. Smetanina; Yu. P. Chuburin. Schrödinger 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/

[1] Dzh. Zaiman, Printsipy teorii tverdogo tela, Mir, M., 1974

[2] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki. T. 4. Analiz operatorov, Mir, M., 1982 | MR

[3] V. Kheine, M. Koen, D. Ueir, Teoriya psevdopotentsiala, Mir, M., 1973

[4] R. R. Gadylshin, TMF, 132 (2002), 97 | DOI | MR | Zbl

[5] Yu. P. Chuburin, Matem. zametki, 52 (1992), 138 | MR

[6] Yu. P. Chuburin, TMF, 72 (1987), 120 | MR

[7] S. Albeverio, F. Gestezi, R. Khöeg-Kron, Kh. Kholden, Reshaemye modeli v kvantovoi mekhanike, Mir, M., 1991 | MR

[8] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki. T. 1. Funktsionalnyi analiz, Mir, M., 1977 | MR

[9] R. Ganning, Kh. Rossi, Analiticheskie funktsii mnogikh kompleksnykh peremennykh, Mir, M., 1969 | MR