R. R. Gadyl'shin, “Local Perturbations of the Schrödinger Operator on the Plane”, TMF, 138:1 (2004), 41–54; Theoret. and Math. Phys., 138:1 (2004), 33

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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 138, Number 1, Pages 41–54
DOI: https://doi.org/10.4213/tmf7 (Mi tmf7)

This article is cited in 14 scientific papers (total in 14 papers)

Local Perturbations of the Schrödinger Operator on the Plane

R. R. Gadyl'shin

Bashkir State Pedagogical University

Full-text PDF (261 kB) Citations (14)

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DOI: https://doi.org/10.4213/tmf7

Abstract: We obtain necessary and sufficient conditions for the appearance of a small eigenvalue of the Schrödinger operator on the plane under local operatorial excitations. In the case where the small eigenvalue exists, we construct its asymptotic behavior. We present examples.

Keywords: Schrödinger operator, perturbation, small parameter, eigenvalue, asymptotic behavior.

Received: 31.07.2002
Revised: 19.03.2003

English version:
Theoretical and Mathematical Physics, 2004, Volume 138, Issue 1, Pages 33–44
DOI: https://doi.org/10.1023/B:TAMP.0000010631.40891.f0

Bibliographic databases:

Language: Russian

Citation: R. R. Gadyl'shin, “Local Perturbations of the Schrödinger Operator on the Plane”, TMF, 138:1 (2004), 41–54; Theoret. and Math. Phys., 138:1 (2004), 33–44

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf7

https://doi.org/10.4213/tmf7

https://www.mathnet.ru/eng/tmf/v138/i1/p41

This publication is cited in the following 14 articles:

Borisov I D., Zezyulin D.A., Znojil M., “Bifurcations of Thresholds in Essential Spectra of Elliptic Operators Under Localized Non-Hermitian Perturbations”, Stud. Appl. Math., 146:4 (2021), 834–880
Golovaty Yu., “Eigenvalues of Schrodinger Operators Near Thresholds: Two Term Approximation”, Methods Funct. Anal. Topol., 26:1 (2020), 76–87
Golovaty Yu.D., “On Coupling Constant Thresholds in One Dimension”, Carpathian Math. Publ., 13:1 (2020), 22–38
M. S. Smetanina, “Asimptotika urovnei operatora Shrëdingera dlya kristallicheskoi plenki s nelokalnym potentsialom”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:4 (2018), 462–473
D. I. Borisov, “Perturbations of the Continuous Spectrum of a Certain Nonlinear Two-Dimensional Operator Sheaf”, J. Math. Sci. (N. Y.), 252:2 (2021), 135–146
D. I. Borisov, M. Znojil, “On eigenvalues of a $\mathscr{P\!T}$ -symmetric operator in a thin layer”, Sb. Math., 208:2 (2017), 173–199
D.I. Borisov, “Estimates of initial scales for layers with small random negative-definite perturbations”, J. Math. Sci. (N. Y.), 241:5 (2019), 518–548
D. I. Borisov, “On the spectrum of a two-dimensional periodic operator with a small localized perturbation”, Izv. Math., 75:3 (2011), 471–505
I. Kh. Khusnullin, “A perturbed boundary eigenvalue problem for the Schrödinger operator on an interval”, Comput. Math. Math. Phys., 50:4 (2010), 646–664
Borisov, D, “The spectrum of two quantum layers coupled by a window”, Journal of Physics A-Mathematical and Theoretical, 40:19 (2007), 5045
A. R. Bikmetov, R. R. Gadyl'shin, “On the spectrum of the Schrödinger operator with large potential concentrated on a small set”, Math. Notes, 79:5 (2006), 729–733
D. I. Borisov, “Discrete spectrum of an asymmetric pair of waveguides coupled through a window”, Sb. Math., 197:4 (2006), 475–504
A. R. Bikmetov, D. I. Borisov, “Discrete Spectrum of the Schrodinger Operator Perturbed by a Narrowly Supported Potential”, Theoret. and Math. Phys., 145:3 (2005), 1691–1702
Borisov D, Exner P, “Exponential splitting of bound states in a waveguide with a pair of distant windows”, Journal of Physics A-Mathematical and General, 37:10 (2004), 3411–3428

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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