Geodesic
Schrödinger operator on the axis with potentials depending on two parameters
Algebra i analiz, Tome 22 (2010) no. 6, pp. 50-66 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Schrödinger operator on the axis is considered; its localized potential is the sum of a small potential and certain potentials with contracting supports, which can increase unboundedly when their supports are contracted. Sufficient conditions are presented for the absence (or existence) of eigenvalues for such an operator. In the case where eigenvalues exist, their asymptotic expansion is constructed.
Keywords: Schrödinger operator
Mots-clés : perturbation. 
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     author = {R. R. Gadyl'shin and I. Kh. Khusnullin},
     title = {Schr\"odinger operator on the axis with potentials depending on two parameters},
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     year = {2010},
     volume = {22},
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     url = {http://geodesic.mathdoc.fr/item/AA_2010_22_6_a2/}
}
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R. R. Gadyl'shin; I. Kh. Khusnullin. Schrödinger operator on the axis with potentials depending on two parameters. Algebra i analiz, Tome 22 (2010) no. 6, pp. 50-66. http://geodesic.mathdoc.fr/item/AA_2010_22_6_a2/

[1] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, v. 3, Kvantovaya mekhanika. Nerelyativistskaya teoriya, Nauka, M., 1974 | MR

[2] Simon B., “The bound state of weakly coupled Schrödinger operators in one and two dimensions”, Ann. Phys., 97 (1976), 279–288 | DOI | MR | Zbl

[3] Klaus M., “On the bound state of Schrödinger operators in one dimension”, Ann. Phys., 108 (1977), 288–300 | DOI | MR | Zbl

[4] Blankenbecler R., Goldberger M. L., Simon B., “The bound states of weakly coupled long-range one-dimensional quantum Hamiltonians”, Ann. Phys., 108 (1977), 69–78 | DOI | MR

[5] Klaus M., Simon B., “Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case”, Ann. Phys., 130 (1980), 251–281 | DOI | MR | Zbl

[6] Borisov D. I., Gadylshin R. R., “O spektre periodicheskogo operatora s malym lokalizovannym vozmuscheniem”, Izv. RAN. Ser. mat., 72:4 (2008), 37–66 | MR | Zbl

[7] Gadylshin R. R., “O lokalnykh vozmuscheniyakh operatora Shrëdingera na osi”, Teor. i mat. fiz., 132:1 (2002), 97–104 | MR | Zbl

[8] Khusnullin I. Kh., “Vozmuschennaya kraevaya zadacha na sobstvennye znacheniya dlya operatora Shrëdingera na otrezke”, Zh. vychisl. mat. i mat. fiz., 50:4 (2010), 679–698

[9] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1976 | MR | Zbl