Abstract:
Expansions in fundamental parabolic bases of the two-dimensional
hydrogen atom in the continuous spectrum are considered. Integral
representations for the coefficients that determine such expansions
are obtained. It is shown that these coefficients can be expressed
in terms of the generalized hypergeometric functions 3F2 of unit
argument.
Citation:
L. S. Davtyan, G. S. Pogosyan, A. N. Sisakyan, V. M. Ter-Antonyan, “Transformations between parabolic bases of the two-dimensional hydrogen atom in the continuous spectrum”, TMF, 74:2 (1988), 240–246; Theoret. and Math. Phys., 74:2 (1988), 157–161
\Bibitem{DavPogSis88}
\by L.~S.~Davtyan, G.~S.~Pogosyan, A.~N.~Sisakyan, V.~M.~Ter-Antonyan
\paper Transformations between parabolic bases of the two-dimensional hydrogen atom in the continuous spectrum
\jour TMF
\yr 1988
\vol 74
\issue 2
\pages 240--246
\mathnet{http://mi.mathnet.ru/tmf4337}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=941748}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 74
\issue 2
\pages 157--161
\crossref{https://doi.org/10.1007/BF01886487}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1988Q165900010}
Linking options:
https://www.mathnet.ru/eng/tmf4337
https://www.mathnet.ru/eng/tmf/v74/i2/p240
This publication is cited in the following 6 articles:
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
Hongcheng Ni, Andreas Becker, “Theoretical analysis of the role of Coulomb interactions in single and double photoionization of the helium dimer using numerical model simulations”, Phys. Rev. A, 89:3 (2014)
Hongcheng Ni, Camilo Ruiz, Reinhard Dörner, Andreas Becker, “Numerical simulations of single-photon double ionization of the helium dimer”, Phys. Rev. A, 88:1 (2013)
C. Grosche, G. S. Pogosyan, A. N. Sissakian, “Path Integral Discussion for Smorodinsky-Winternitz Potentials: I. Two- and Three Dimensional Euclidean Space”, Fortschr. Phys., 43:6 (1995), 453
Christian Grosche, “Path Integration and Separation of Variables in Spaces of Constant Curvature in Two and Three Dimensions”, Fortschr. Phys., 42:6 (1994), 509
X. L. Yang, S. H. Guo, F. T. Chan, K. W. Wong, W. Y. Ching, “Analytic solution of a two-dimensional hydrogen atom. I. Nonrelativistic theory”, Phys. Rev. A, 43:3 (1991), 1186
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