Abstract:
It is shown that both the nonrelativistic and the relativistic problems for the hydrogen atom can be formulated in terms of the generators of the noncompact algebra O(2,1). The possible values of the energy (the Balmer and Sommerfeld formulas, respectively), can be determined by an appropriate choice of the basis (tilt) for the generators in the algebra O(2,1).
Citation:
V. F. Dmitriev, Yu. B. Rumer, “O(2,1) Algebra and the hydrogen atom”, TMF, 5:2 (1970), 276–280; Theoret. and Math. Phys., 5:2 (1970), 1146–1149
\Bibitem{DmiRum70}
\by V.~F.~Dmitriev, Yu.~B.~Rumer
\paper $O(2,1)$~Algebra and the hydrogen atom
\jour TMF
\yr 1970
\vol 5
\issue 2
\pages 276--280
\mathnet{http://mi.mathnet.ru/tmf4207}
\transl
\jour Theoret. and Math. Phys.
\yr 1970
\vol 5
\issue 2
\pages 1146--1149
\crossref{https://doi.org/10.1007/BF01036108}
Linking options:
https://www.mathnet.ru/eng/tmf4207
https://www.mathnet.ru/eng/tmf/v5/i2/p276
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Sami Ghazouani, Sboui Insaf, “Superintegrability of the Dunkl–Coulomb problem in three-dimensions”, J. Phys. A: Math. Theor., 53:3 (2020), 035202
Marisol Bermúdez-Montaña, Marisol Rodríguez-Arcos, Renato Lemus, José M. Arias, Joaquín Gómez-Camacho, Emilio Orgaz, “Algebraic DVR Approaches Applied to Describe the Stark Effect”, Symmetry, 12:10 (2020), 1719
R. N. Lee, A. I. Milstein, I. S. Terekhov, “Relativistic Coulomb Green's function in d dimensions”, J. Exp. Theor. Phys., 113:2 (2011), 202
Sh. M. Nagiyev, “Dynamical symmetry group of the relativistic Coulomb problem in the quasipotential approach”, Theoret. and Math. Phys., 80:1 (1989), 697–702
I. V. Bogdanov, “Inverse problem of mechanics in momentum space”, Soviet Physics Journal, 28:1 (1985), 40
A.I. Mil'shtein, V.M. Strakhovenko, “The O(2.1) algebra and the electron green function in a Coulomb field”, Physics Letters A, 90:9 (1982), 447
J. Čížek, J. Paldus, “An algebraic approach to bound states of simple one‐electron systems”, Int J of Quantum Chemistry, 12:5 (1977), 875
M Bednář, “Algebraic treatment of quantum-mechanical models with modified Coulomb potentials”, Annals of Physics, 75:2 (1973), 305
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