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TMF, 1984, Volume 61, Number 1, Pages 99–117 (Mi tmf5662)  

This article is cited in 5 scientific papers (total in 5 papers)

Two-dimensional hydrogen atom. I. Elliptic basis

L. G. Mardoyan, G. S. Pogosyan, A. N. Sisakyan, V. M. Ter-Antonyan


Abstract: A two-dimensional hydrogen atom is analyzed in elliptic coordinates. Separation of the variables reduces the problem to the solution of the Ince equation in the complex plane subject to certain boundary conditions. It is shown that in the limits $R\rightarrow 0$ and $R\rightarrow\infty$ ($R$ is a parameter that specifies the elliptic coordinates) the obtained solutions go over to polar and parabolic bases, respectively. The explicit form of the elliptic basis is given for the lowest quantum states.

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English version:
Theoretical and Mathematical Physics, 1984, 61:1, 1021–1034

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Received: 28.07.1983

Citation: L. G. Mardoyan, G. S. Pogosyan, A. N. Sisakyan, V. M. Ter-Antonyan, “Two-dimensional hydrogen atom. I. Elliptic basis”, TMF, 61:1 (1984), 99–117; Theoret. and Math. Phys., 61:1 (1984), 1021–1034

Citation in format AMSBIB
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\by L.~G.~Mardoyan, G.~S.~Pogosyan, A.~N.~Sisakyan, V.~M.~Ter-Antonyan
\paper Two-dimensional hydrogen atom. I. Elliptic basis
\jour TMF
\yr 1984
\vol 61
\issue 1
\pages 99--117
\mathnet{http://mi.mathnet.ru/tmf5662}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=774211}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 61
\issue 1
\pages 1021--1034
\crossref{https://doi.org/10.1007/BF01038551}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984AGK6100010}


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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. L. G. Mardoyan, G. S. Pogosyan, A. N. Sisakyan, V. M. Ter-Antonyan, “Interbasis expansions in the two-dimensional hydrogen atom”, Theoret. and Math. Phys., 63:3 (1985), 597–603  mathnet  crossref  mathscinet  isi
    2. L. S. Davtyan, G. S. Pogosyan, A. N. Sisakyan, V. M. Ter-Antonyan, “Two-dimensional hydrogen atom. Reciprocal expansions of the polar and parabolic bases of the continuous spectrum”, Theoret. and Math. Phys., 66:2 (1986), 146–153  mathnet  crossref  mathscinet  isi
    3. Pogosyan, G, “Separation of variables and Lie algebra contractions. Applications to special functions”, Physics of Particles and Nuclei, 33 (2002), S123  isi
    4. D. I. Bondar, M. Gnatich, V. Yu. Lazur, “Two-dimensional problem of two Coulomb centers at small intercenter distances”, Theoret. and Math. Phys., 148:2 (2006), 1100–1116  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. V. V. Pupyshev, “Two-dimensional Coulomb scattering of a quantum particle: Wave functions and Green's functions”, Theoret. and Math. Phys., 186:2 (2016), 213–230  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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