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Russian Physics Journal

, Volume 61, Issue 2, pp 312–320 | Cite as

Characteristics of a Two-Dimensional Hydrogen-like Atom

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Using the customary and well-known representation of the radiation probability of a hydrogen-like atom in the three-dimensional case, a general expression for the probability of single-photon emission of a twodimensional atom has been obtained along with an expression for the particular case of the transition from the first excited state to the ground state, in the latter case in comparison with corresponding expressions for the three-dimensional atom and the one-dimensional atom. Arguments are presented in support of the claim that this method of calculation gives a value of the probability that is identical to the value given by exact methods of QED extended to the subspace {0, 1, 2}. Relativistic corrections ~ (Zα)4 to the usual Schrödinger value of the energy (~ (Zα)2) are also discussed.

Keywords

two-dimensional hydrogen atom radiation energy corrections 

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References

  1. 1.
    H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms, Plenum Publishing, New York (1977).Google Scholar
  2. 2.
    V. V. Skobelev, Zh. Eksp. Teor. Fiz., 149, No. 2, 285 (2016); correction: Zh. Eksp. Teor. Fiz., 149, No. 4, 909 (2016).Google Scholar
  3. 3.
    V. V. Skobelev, Russ. Phys. J., 59, No. 1, 48 (2016).CrossRefGoogle Scholar
  4. 4.
    A. A. Sokolov, Yu. M. Loskutov, and I. M. Ternov, Quantum Mechanics, Holt, Rinehart & Winston, Austin (1966).MATHGoogle Scholar
  5. 5.
    A. Gorlitz et al., Phys. Rev. Lett., 87, 130402 (2001).ADSCrossRefGoogle Scholar
  6. 6.
    V. V. Skobelev, Zh. Eksp. Teor. Fiz., 151, No. 6, 1031 (2017).Google Scholar
  7. 7.
    R. London, Amer. J. Phys., 27, 649 (1959).ADSCrossRefGoogle Scholar
  8. 8.
    L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-Relativistic Theory), Vol. 3, Pergamon Press, Oxford (1977).MATHGoogle Scholar
  9. 9.
    B. Zaslow and C. E. Zandler, Amer. J. Phys., 35, 1118 (1967).ADSCrossRefGoogle Scholar
  10. 10.
    A. Cisneros and N. V. McIntosh, J. Math. Phys., 10, 277 (1968).ADSCrossRefGoogle Scholar
  11. 11.
    L. G. Mardoyan, G. S. Pogosyan, A. S. Sisakyan, and V. M. Ter-Antonyan, Teor. Mat. Fiz., 61, 99 (1984).CrossRefGoogle Scholar
  12. 12.
    V. V. Skobelev, Russ. Phys. J., 59, No. 7, 1076 (2016).CrossRefGoogle Scholar
  13. 13.
    V. V. Skobelev, Russ. Phys. J., 60, No. 7, 1133 (2017).CrossRefGoogle Scholar
  14. 14.
    A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics, Nauka, Moscow (1969).Google Scholar
  15. 15.
    V. V. Skobelev, Russ. Phys. J., 59, No. 10, 1623 (2016); 60, No. 1, 50 (2017).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Moscow Polytechnic UniversityMoscowRussia

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