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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 135, Number 3, Pages 427–433
DOI: https://doi.org/10.4213/tmf198 (Mi tmf198) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Coulomb Problem in a One-Dimensional Space with Constant Positive Curvature

L. G. Mardoyana, G. S. Pogosyanab, A. N. Sisakyanb

a Yerevan State University
b Joint Institute for Nuclear Research
Full-text PDF (182 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf198
Abstract: We construct a complex transformation S1C→S1 generalizing the known Hurwitz transformation in the Euclidean space for one-dimensional quantum mechanics. As in the case of the flat space, this transformation allows establishing the connection between the Coulomb problem and the oscillator problem with the Calogero–Sutherland potential added. We fully describe the motion in a Coulomb field in S1 and determine the energy spectrum and the wave functions with the correct normalizing constant.
Keywords: one-dimensional hydrogen atom, Schrödinger equation, Hurwitz transformation, constant-curvature space.
English version:
Theoretical and Mathematical Physics, 2003, Volume 135, Issue 3, Pages 808–813
DOI: https://doi.org/10.1023/A:1024078803869
Bibliographic databases:
Language: Russian
Citation: L. G. Mardoyan, G. S. Pogosyan, G. S. Pogosyan, A. N. Sisakyan, “Coulomb Problem in a One-Dimensional Space with Constant Positive Curvature”, TMF, 135:3 (2003), 427–433; Theoret. and Math. Phys., 135:3 (2003), 808–813
Citation in format AMSBIB
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\by L.~G.~Mardoyan, G.~S.~Pogosyan, G.~S.~Pogosyan, A.~N.~Sisakyan
\paper Coulomb Problem in a One-Dimensional Space with Constant Positive Curvature
\jour TMF
\yr 2003
\vol 135
\issue 3
\pages 427--433
\mathnet{http://mi.mathnet.ru/tmf198}
\crossref{https://doi.org/10.4213/tmf198}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1984447}
\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 135
\issue 3
\pages 808--813
\crossref{https://doi.org/10.1023/A:1024078803869}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000184367300006}
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  • https://www.mathnet.ru/eng/tmf198
  • https://doi.org/10.4213/tmf198
  • https://www.mathnet.ru/eng/tmf/v135/i3/p427
    • This publication is cited in the following 4 articles:
    1. Arsen Shutovskyi, Vasyl Sakhnyuk, Vadim Muliar, “Solving a singular integral equation for the one-dimensional Coulomb problem”, Phys. Scr., 98:8 (2023), 085219  crossref
    2. Dunn, C, “Spectral geometry, homogeneous spaces and differential forms with finite Fourier series”, Journal of Physics A-Mathematical and Theoretical, 41:13 (2008), 135204  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Pogosyan GS, Vicent LE, Wolf KB, “Quantum phase space for the one-dimensional hydrogen atom on the hyperbola”, Journal of Mathematical Physics, 46:7 (2005), 072108  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Burdik C., Pogosyan G.S., “Two exactly-solvable problems in one-dimensional hyperbolic space”, Lie Theory and its Applications in Physics V, Proceedings, 2004, 294–300  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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