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TMF, 2003, Volume 134, Number 3, Pages 447–459 (Mi tmf160)  

This article is cited in 11 scientific papers (total in 11 papers)

The Spectrum of the Two-Dimensional Periodic Schrödinger Operator

L. I. Danilov

Physical-Technical Institute of the Ural Branch of the Russian Academy of Sciences

Abstract: The absence of eigenvalues (of infinite multiplicity) for the two-dimensional periodic Schrödinger operator with a variable metric is proved. The method of proof does not use the change of variables reducing the metric to a scalar form.

Keywords: Schrödinger operator, spectrum, periodic electric potential, periodic magnetic potential, variable metric

DOI: https://doi.org/10.4213/tmf160

Full text: PDF file (273 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2003, 134:3, 392–403

Bibliographic databases:

Received: 10.01.2002
Revised: 13.06.2002

Citation: L. I. Danilov, “The Spectrum of the Two-Dimensional Periodic Schrödinger Operator”, TMF, 134:3 (2003), 447–459; Theoret. and Math. Phys., 134:3 (2003), 392–403

Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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\pages 392--403
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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. L. I. Danilov, “Ob otsutstvii sobstvennykh znachenii v spektre dvumernykh periodicheskikh operatorov Diraka i Shredingera”, Izv. IMI UdGU, 2004, no. 1(29), 49–84  mathnet
    2. L. I. Danilov, “The absence of eigenvalues in the spectrum of ageneralized two-dimensional periodic Dirac operator”, St. Petersburg Math. J., 17:3 (2006), 409–433  mathnet  crossref  mathscinet  zmath
    3. L. I. Danilov, “Ob absolyutnoi nepreryvnosti spektra trekhmernogo periodicheskogo operatora Diraka”, Izv. IMI UdGU, 2006, no. 1(35), 49–76  mathnet
    4. Shen, ZW, “Uniform Sobolev inequalities and absolute continuity of periodic operators”, Transactions of the American Mathematical Society, 360:4 (2008), 1741  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Danilov, LI, “On absolute continuity of the spectrum of a periodic magnetic Schrodinger operator”, Journal of Physics A-Mathematical and Theoretical, 42:27 (2009), 275204  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Danilov L.I., “On absolute continuity of the spectrum of three- and four-dimensional periodic Schrodinger operators”, J. Phys. A: Math. Theor., 43:21 (2010), 215201  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. L. I. Danilov, “O spektre periodicheskogo operatora Shredingera s potentsialom iz prostranstva Morri”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 3, 25–47  mathnet
    8. L. I. Danilov, “O spektre dvumernogo obobschennogo periodicheskogo operatora Shredingera”, Izv. IMI UdGU, 2013, no. 1(41), 78–95  mathnet
    9. L. I. Danilov, “O spektre dvumernogo obobschennogo periodicheskogo operatora Shredingera. II”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 3–28  mathnet
    10. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
    11. L. I. Danilov, “O spektre dvumernogo operatora Shredingera s odnorodnym magnitnym polem i periodicheskim elektricheskim potentsialom”, Izv. IMI UdGU, 51 (2018), 3–41  mathnet  crossref  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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