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 TMF, 1983, Volume 57, Number 2, Pages 304–313 (Mi tmf2263)

Spectrum and eigenfunctions of Schrödinger operator with zero-range potential of homogeneous lattice type in three-dimensional space

Yu. E. Karpeshina

Abstract: A study is made of the spectrum and all eigenfunctions of a Schrödinger operator with zero-range potential of the type of a homogeneous infinite rectangular lattice in three-dimensional space.

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English version:
Theoretical and Mathematical Physics, 1983, 57:2, 1156–1162

Bibliographic databases:

Citation: Yu. E. Karpeshina, “Spectrum and eigenfunctions of Schrödinger operator with zero-range potential of homogeneous lattice type in three-dimensional space”, TMF, 57:2 (1983), 304–313; Theoret. and Math. Phys., 57:2 (1983), 1156–1162

Citation in format AMSBIB
\Bibitem{Kar83} \by Yu.~E.~Karpeshina \paper Spectrum and eigenfunctions of Schr\"odinger operator with zero-range potential of homogeneous lattice type in three-dimensional space \jour TMF \yr 1983 \vol 57 \issue 2 \pages 304--313 \mathnet{http://mi.mathnet.ru/tmf2263} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=734891} \transl \jour Theoret. and Math. Phys. \yr 1983 \vol 57 \issue 2 \pages 1156--1162 \crossref{https://doi.org/10.1007/BF01018661} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983SX71000014} 

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Citing articles on Google Scholar: Russian citations, English citations
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1. V. A. Geiler, V. A. Margulis, “Anderson localization in the nondiscrete maryland model”, Theoret. and Math. Phys., 70:2 (1987), 133–140
2. P. B. Kurasov, B. S. Pavlov, “Electron in a homogeneous crystal of point atoms with internal structure. II”, Theoret. and Math. Phys., 74:1 (1988), 58–66
3. V. A. Geiler, V. V. Demidov, “Spectrum of three-dimensional landau operator perturbed by a periodic point potential”, Theoret. and Math. Phys., 103:2 (1995), 561–569
4. J. Brüning, V. A. Geiler, “Gauge-periodic point perturbations on the Lobachevsky plane”, Theoret. and Math. Phys., 119:3 (1999), 687–697
5. Albeverio, S, “The band structure of the general periodic Schrodinger operator with point interactions”, Communications in Mathematical Physics, 210:1 (2000), 29
6. Bruning J., Geyler V.A., “The spectrum of periodic point perturbations and the Krein resolvent formula”, Differential Operators and Related Topics, Operator Theory : Advances and Applications, 117, 2000, 71–86
7. Kuchment, P, “On the structure of spectra of periodic elliptic operators”, Transactions of the American Mathematical Society, 354:2 (2001), 537
8. Bruning, J, “Scattering on compact manifolds with infinitely thin horns”, Journal of Mathematical Physics, 44:2 (2003), 371
9. 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
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