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TMF, 1994, Volume 98, Number 1, Pages 38–47 (Mi tmf1399)  

This article is cited in 8 scientific papers (total in 8 papers)

Solutions of the Schrödinger equation in the case of a semiinfinite crystal

Yu. P. Chuburin

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

Abstract: It is proved that the bounded solutions of the Bloch type in $x_1$, $x_2$ variables of the Schrödinger equation with the potential which is periodic in the semi-space $\{x_3\geqslant 0\}$ and exponentially decreases when $x_3\to -\infty$, may be approximated by the solutions of the Schrödinger equation which correspond to crystal films with a number of layers tending to infinity. It gives the possibility to find the number of linearly independent solutions of this type under some propositions.

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English version:
Theoretical and Mathematical Physics, 1994, 98:1, 27–33

Bibliographic databases:

Received: 07.12.1992

Citation: Yu. P. Chuburin, “Solutions of the Schrödinger equation in the case of a semiinfinite crystal”, TMF, 98:1 (1994), 38–47; Theoret. and Math. Phys., 98:1 (1994), 27–33

Citation in format AMSBIB
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\by Yu.~P.~Chuburin
\paper Solutions of the Schr\"odinger equation in the case of a~semiinfinite crystal
\jour TMF
\yr 1994
\vol 98
\issue 1
\pages 38--47
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1291365}
\zmath{https://zbmath.org/?q=an:0817.35085}
\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 98
\issue 1
\pages 27--33
\crossref{https://doi.org/10.1007/BF01015120}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994NV61800004}


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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. Yu. P. Chuburin, “On Schrodinger equation for the plane film with the limit periodic lattice”, Theoret. and Math. Phys., 106:1 (1996), 108–117  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Yu. P. Chuburin, “On approximation of the “Membrane” Schrödinger operator by the “Crystal” operator”, Math. Notes, 62:5 (1997), 648–654  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Yu. P. Chuburin, “On small perturbations of the Schrödinger equation with periodic potential”, Theoret. and Math. Phys., 110:3 (1997), 351–359  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Chuburin, YP, “On levels of a weakly perturbed periodic Schrodinger operator”, Communications in Mathematical Physics, 249:3 (2004), 497  crossref  mathscinet  zmath  adsnasa  isi
    5. 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
    6. 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
    7. 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
    8. T. S. Tinyukova, “Issledovanie raznostnogo uravneniya Shredingera dlya nekotorykh fizicheskikh modelei”, Izv. IMI UdGU, 2013, no. 2(42), 3–57  mathnet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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