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TMF, 1997, Volume 110, Number 3, Pages 443–453 (Mi tmf980)  

This article is cited in 16 scientific papers (total in 16 papers)

On small perturbations of the Schrödinger equation with periodic potential

Yu. P. Chuburin

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

Abstract: We consider small perturbations of the potential periodic in variables $x_j$, $j=1,2,3$, by a function wich is periodic in $x_1$, $x_2$ and exponentially decreases as $|x_3|\to\infty$. We prove that close to energies corresponding to the extrema in the third component of the quasy-momentum of nondegenerate eigenvalues of the Schrödinger operator with periodic potential considered in the cell there exists a unique (up to multiplicative factor) solution of the integral equation describing both eigenvalues and resonance levels. The asymptotic behaviour of the latter quantities is described.

DOI: https://doi.org/10.4213/tmf980

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English version:
Theoretical and Mathematical Physics, 1997, 110:3, 351–359

Bibliographic databases:

Received: 14.10.1996

Citation: Yu. P. Chuburin, “On small perturbations of the Schrödinger equation with periodic potential”, TMF, 110:3 (1997), 443–453; Theoret. and Math. Phys., 110:3 (1997), 351–359

Citation in format AMSBIB
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\by Yu.~P.~Chuburin
\paper On small perturbations of the Schr\"odinger equation with periodic potential
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\yr 1997
\vol 110
\issue 3
\pages 443--453
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\crossref{https://doi.org/10.4213/tmf980}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1471189}
\zmath{https://zbmath.org/?q=an:0913.47013}
\transl
\jour Theoret. and Math. Phys.
\yr 1997
\vol 110
\issue 3
\pages 351--359
\crossref{https://doi.org/10.1007/BF02630460}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. P. Chuburin, “Resonance multiplicity of a perturbed periodic Schrödinger operator”, Theoret. and Math. Phys., 116:1 (1998), 846–855  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Vol'f, GV, “Resonance states of the continuous spectrum of a bounded crystal near the critical points of volume bands”, Physics of the Solid State, 40:11 (1998), 1813  crossref  adsnasa  isi  scopus  scopus  scopus
    3. Yu. P. Chuburin, “Schrödinger operator with a perturbed small steplike potential”, Theoret. and Math. Phys., 120:2 (1999), 1045–1057  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Yu. P. Chuburin, “Schrödinger operator eigenvalue (resonance) on a zone boundary”, Theoret. and Math. Phys., 126:2 (2001), 161–168  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Chuburin, YP, “On levels of a weakly perturbed periodic Schrodinger operator”, Communications in Mathematical Physics, 249:3 (2004), 497  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    6. L. E. Morozova, Yu. P. Chuburin, “Ob urovnyakh odnomernogo diskretnogo operatora Shredingera s ubyvayuschim potentsialom”, Izv. IMI UdGU, 2004, no. 1(29), 85–94  mathnet
    7. N. I. Pletnikova, “Ob odnomernom uravnenii Shredingera s nelokalnym potentsialom tipa vozmuschennoi stupenki”, Izv. IMI UdGU, 2004, no. 1(29), 95–108  mathnet
    8. Yu. P. Chuburin, “Perturbation Theory of Resonances and Embedded Eigenvalues of the Schrodinger Operator For a Crystal Film”, Theoret. and Math. Phys., 143:3 (2005), 836–847  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Wolf, GV, “Specific features of low-energy electron scattering by thin films of cubic crystals”, Physics of the Solid State, 47:6 (2005), 1048  crossref  adsnasa  isi  scopus  scopus  scopus
    10. Yu. P. Chuburin, “Decay law for a quasistationary state of the Schrödinger operator for a crystal film”, Theoret. and Math. Phys., 151:2 (2007), 648–658  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. Baranova, LY, “Quasi-levels of the two-particle discrete Schrodinger operator with a perturbed periodic potential”, Journal of Physics A-Mathematical and Theoretical, 41:43 (2008), 435205  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    12. L. E. Baranova, Yu. P. Chuburin, “Kvaziurovni dvukhchastichnogo diskretnogo operatora Shredingera s malym potentsialom”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2008, no. 1, 35–46  mathnet
    13. Yu. P. Chuburin, “Quasilevels of a two-particle Schrödinger operator with a perturbed periodic potential”, Theoret. and Math. Phys., 158:1 (2009), 96–104  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    14. T. S. Tinyukova, Yu. P. Chuburin, “Electron scattering by a crystal layer”, Theoret. and Math. Phys., 176:3 (2013), 1207–1219  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. T. S. Tinyukova, “Issledovanie raznostnogo uravneniya Shredingera dlya nekotorykh fizicheskikh modelei”, Izv. IMI UdGU, 2013, no. 2(42), 3–57  mathnet
    16. Yu. P. Chuburin, “Two-particle scattering in a periodic medium”, Theoret. and Math. Phys., 191:2 (2017), 738–751  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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