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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 4, Pages 667–682 (Mi zvmmf487)  

This article is cited in 5 scientific papers (total in 5 papers)

Asymptotics of eigenelements of boundary value problems for the Schrödinger operator with a large potential localized on a small set

A. R. Bikmetov

Bashkortostan State Pedagogical University, ul. Oktyabrskoi Revolyutsii 3a, Ufa, 450000, Bashkortostan, Russia

Abstract: Asymptotics of eigenelements of a singularly perturbed boundary value problem for the three-dimensional Schrödinger operator is constructed in a bounded domain with the Dirichlet and Neumann boundary condition. The perturbation is described by a large potential whose support contracts into a point. In the case of the Dirichlet boundary conditions, this problem corresponds to a potential well with infinitely high walls and a narrow finite peak at the bottom.

Key words: three-dimensional Schrödinger operator, eigenvalues, singular perturbation.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:4, 636–650

Bibliographic databases:

Document Type: Article
UDC: 519.634
Received: 18.07.2005

Citation: A. R. Bikmetov, “Asymptotics of eigenelements of boundary value problems for the Schrödinger operator with a large potential localized on a small set”, Zh. Vychisl. Mat. Mat. Fiz., 46:4 (2006), 667–682; Comput. Math. Math. Phys., 46:4 (2006), 636–650

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

    This publication is cited in the following articles:
    1. Chechkin G.A., Koroleva Yu.O., Meidell A., Persson L.-E., “On the Friedrichs inequality in a domain perforated aperiodically along the boundary. Homogenization procedure. Asymptotics for parabolic problems”, Russian Journal of Mathematical Physics, 16:1 (2009), 1–16  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. I. Kh. Khusnullin, “A perturbed boundary eigenvalue problem for the Schrödinger operator on an interval”, Comput. Math. Math. Phys., 50:4 (2010), 646–664  mathnet  crossref  mathscinet  adsnasa  isi
    3. Gadyl'shin R.R., “On Regular and Singular Perturbations of the Eigenelements of the Laplacian”, Integral Methods in Science and Engineering, 2010, 135–148  crossref  mathscinet  zmath  isi
    4. A. R. Bikmetov, R. R. Gadylshin, “Vozmuschenie ellipticheskogo operatora uzkim potentsialom v $n$-mernoi oblasti”, Ufimsk. matem. zhurn., 4:2 (2012), 28–64  mathnet  mathscinet
    5. D.I. Borisov, R. Kh. Karimov, T. F. Sharapov, “Initial length scale estimate for waveguides with some random singular potentials”, Ufa Math. J., 7:2 (2015), 33–54  mathnet  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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