RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2004, Volume 138, Number 1, Pages 41–54 (Mi tmf7)  

This article is cited in 9 scientific papers (total in 9 papers)

Local Perturbations of the Schrödinger Operator on the Plane

R. R. Gadyl'shin

Bashkir State Pedagogical University

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

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

Full text: PDF file (261 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2004, 138:1, 33–44

Bibliographic databases:

Received: 31.07.2002
Revised: 19.03.2003

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
\Bibitem{Gad04}
\by R.~R.~Gadyl'shin
\paper Local Perturbations of the Schr\"odinger Operator on the Plane
\jour TMF
\yr 2004
\vol 138
\issue 1
\pages 41--54
\mathnet{http://mi.mathnet.ru/tmf7}
\crossref{https://doi.org/10.4213/tmf7}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2061091}
\zmath{https://zbmath.org/?q=an:1178.35146}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2004TMP...138...33G}
\transl
\jour Theoret. and Math. Phys.
\yr 2004
\vol 138
\issue 1
\pages 33--44
\crossref{https://doi.org/10.1023/B:TAMP.0000010631.40891.f0}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000188977100004}


Linking options:
  • http://mi.mathnet.ru/eng/tmf7
  • https://doi.org/10.4213/tmf7
  • http://mi.mathnet.ru/eng/tmf/v138/i1/p41

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. 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  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. D. I. Borisov, “Discrete spectrum of an asymmetric pair of waveguides coupled through a window”, Sb. Math., 197:4 (2006), 475–504  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Borisov, D, “The spectrum of two quantum layers coupled by a window”, Journal of Physics A-Mathematical and Theoretical, 40:19 (2007), 5045  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. 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
    7. D. I. Borisov, “On the spectrum of a two-dimensional periodic operator with a small localized perturbation”, Izv. Math., 75:3 (2011), 471–505  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. D. I. Borisov, M. Znojil, “On eigenvalues of a $\mathscr{PT}$-symmetric operator in a thin layer”, Sb. Math., 208:2 (2017), 173–199  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. 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  mathnet  crossref  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:295
    Full text:95
    References:42
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019