Geodesic
Local Perturbations of Quantum Waveguides
Teoretičeskaâ i matematičeskaâ fizika, Tome 145 (2005) no. 3, pp. 358-371 Cet article a éte moissonné depuis la source Math-Net.Ru

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We give necessary and sufficient conditions for the occurrence of eigenvalues of the Schrodinger operator in strips and cylinders under small localized perturbations. We construct asymptotic approximations for the eigenvalues.
Keywords: Schrodinger operator, waveguide, spectrum, asymptotic approximation.
Mots-clés : perturbation 
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R. R. Gadyl'shin. Local Perturbations of Quantum Waveguides. Teoretičeskaâ i matematičeskaâ fizika, Tome 145 (2005) no. 3, pp. 358-371. http://geodesic.mathdoc.fr/item/TMF_2005_145_3_a3/

[1] V. P. Maslov, DAN SSSR, 123:4 (1958), 631 ; В. П. Маслов, Е. М. Воробьев, ДАН СССР, 179:3 (1968), 558 | Zbl

[2] P. Exner, P. Šeba, J. Math. Phys., 30 (1989), 2574 ; P. Exner, J. Math. Phys., 34 (1993), 23 | DOI | MR | Zbl | DOI | MR | Zbl

[3] P. Duclos, P. Exner, Rev. Math. Phys., 7 (1995), 73 | DOI | MR | Zbl

[4] W. Bulla, F. Gesztesy, W. Renger, B. Simon, Proc. Amer. Math. Soc., 127 (1997), 1487 | DOI | MR

[5] R. R. Gadylshin, “O sobstvennom znachenii zadachi Dirikhle v lokalno vozmuschennom tsilindre”, Uchenye zapiski, Sbornik nauchnykh trudov, no. 3, ed. Z. Sh. Karimov, Izd-vo Bashkirskogo gosudarstvennogo pedagogicheskogo universiteta, Ufa, 2001, 38

[6] P. Exner, S. A. Vugalter, Lett. Math. Phys., 39 (1997), 59 | DOI | MR | Zbl

[7] D. Borisov, P. Exner, R. Gadyl'shin, D. Krejcirik, Ann. Henry Poincaré, 2 (2001), 553 | DOI | MR | Zbl

[8] V. V. Grushin, Matem. zametki, 75 (2004), 360 | DOI | MR | Zbl

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