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Trudy Inst. Mat. i Mekh. UrO RAN, 2003, Volume 9, Number 1, Pages 15–25 (Mi timm253)  

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

Asymptotic solutions of the Schrödinger equation in thin tubes

V. V. Belov, S. Yu. Dobrokhotov, S. O. Sinitsyn


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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2003, suppl. 1, S13–S23

Bibliographic databases:
Received: 30.10.2002

Citation: V. V. Belov, S. Yu. Dobrokhotov, S. O. Sinitsyn, “Asymptotic solutions of the Schrödinger equation in thin tubes”, Asymptotic expansions, approximation theory, topology, Trudy Inst. Mat. i Mekh. UrO RAN, 9, no. 1, 2003, 15–25; Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S13–S23

Citation in format AMSBIB
\Bibitem{BelDobSin03}
\by V.~V.~Belov, S.~Yu.~Dobrokhotov, S.~O.~Sinitsyn
\paper Asymptotic solutions of the Schr\"odinger equation in thin tubes
\inbook Asymptotic expansions, approximation theory, topology
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2003
\vol 9
\issue 1
\pages 15--25
\mathnet{http://mi.mathnet.ru/timm253}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2093426}
\zmath{https://zbmath.org/?q=an:1126.35354}
\elib{http://elibrary.ru/item.asp?id=12226573}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2003
\issue , suppl. 1
\pages S13--S23


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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. V. V. Grushin, “On the Eigenvalues of Finitely Perturbed Laplace Operators in Infinite Cylindrical Domains”, Math. Notes, 75:3 (2004), 331–340  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. V. Belov, S. Yu. Dobrokhotov, T. Ya. Tudorovskii, “Asymptotic Solutions of Nonrelativistic Equations of Quantum Mechanics in Curved Nanotubes: I. Reduction to Spatially One-Dimensional Equations”, Theoret. and Math. Phys., 141:2 (2004), 1562–1592  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Belov V.V., Dobrokhotov S.Y., Tudorovskii T.Y., “Quantum and classical dynamics of an electron in thin curved tubes with spin and external electromagnetic fields taken into account”, Russian Journal of Mathematical Physics, 11:1 (2004), 109–119  mathscinet  zmath  isi
    4. V. V. Grushin, “Asymptotic Behavior of the Eigenvalues of the Schrödinger Operator with Transversal Potential in a Weakly Curved Infinite Cylinder”, Math. Notes, 77:5 (2005), 606–613  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Belov V.V., Dobrokhotov S.Yu., Tudorovskiy T.Ya., “Operator separation of variables for adiabatic problems in quantum and wave mechanics”, Journal of Engineering Mathematics, 55:1–4 (2006), 183–237  crossref  mathscinet  zmath  isi  scopus
    6. V. V. Grushin, “Asymptotic Behavior of the Eigenvalues of the Schrödinger Operator in Thin Closed Tubes”, Math. Notes, 83:4 (2008), 463–477  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. V. V. Grushin, “Asymptotic Behavior of Eigenvalues of the Laplace Operator in Thin Infinite Tubes”, Math. Notes, 85:5 (2009), 661–673  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Borisov D., Cardone G., “Planar waveguide with “twisted” boundary conditions: Small width”, J Math Phys, 53:2 (2012), 023503  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. D.I. Borisov, “The Emergence of Eigenvalues of a $\mathcal{PT}$-Symmetric Operator in a Thin Strip”, Math. Notes, 98:6 (2015), 872–883  mathnet  crossref  crossref  mathscinet  isi  elib
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