A model-dependent approach to the non-relativistic Lamb shift

  • J. F. Diaz-ValdesEmail author
  • S. A. Bruce
Regular Article


The precise observation of the Lamb shift, between the \(2s_{1/2}\) and \(2p_{1/2}\) levels in hydrogen, was a genuine motivation for the development of modern quantum electrodynamics. According to Dirac theory, the \(2s_{1/2}\) and \(2p_{1/2}\) levels should have equal energies. However, “radiative corrections” due to the interaction between the atomic electron and the vacuum, shift the \(2s_{1/2}\) level higher in energy by around \(4.37493\times 10^{-6}\) eV or \( 2\pi\hbar\times 1057.85\) MHz relative to the \(2p_{1/2}\) level. The measurement of Lamb and Retherford provided the stimulus for renormalization theory which has been so successful in handling troublesome divergences. The Lamb shift is still a central theme in atomic physics. W.E. Lamb was the first to see that this tiny shift, so elusive and hard to measure, would clarify in a fundamental way our thinking about particles and fields. In this article, the Lamb shift for the 2s energy level in hydrogen is assessed for three different electron models by using the variational principle. It is then verified that this shift arises mostly from the interaction of a bound electron with the zero-point fluctuations of the free electromagnetic field (Welton’s interpretation). We briefly comment on the construct validity of the proposed electron models.


  1. 1.
    J.J. Sakurai Advanced Quantum Mechanics (The Benjamin/Cummings Publishing Company, Inc., 1984)Google Scholar
  2. 2.
    W.E. Lamb jr., R.C. Retherford, Phys. Rev. 72, 241 (1947)ADSCrossRefGoogle Scholar
  3. 3.
    G.W.F. Drake, Adv. At. Mol. Phys. 18, 399 (1982)ADSCrossRefGoogle Scholar
  4. 4.
    P. Burikham, K. Cheamsawat, T. Harko, M.J. Lake, Eur. Phys. J. C 76, 106 (2016)ADSCrossRefGoogle Scholar
  5. 5.
    C.G. Böhmer, T. Harko, Found. Phys. 38, 216 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    J.F. Diaz-Valdes, S.A. Bruce, Eur. Phys. J. Plus 132, 138 (2017)CrossRefGoogle Scholar
  7. 7.
    Steven Weinberg, arXiv:0903.0568Google Scholar
  8. 8.
    T.A. Welton, Phys. Rev. 74, 1167 (1948)ADSCrossRefGoogle Scholar
  9. 9.
    Marlan O. Scully, M. Suhail Zubairy, Quantum Optics (Cambridge University Press, Cambridge UK, 1997) pp. 13--16Google Scholar
  10. 10.
    J.D. Bjorken, S.D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, Inc., New York, 1964) pp. 59--60Google Scholar
  11. 11.
    D.J. Gross, Lectures on Quantum Field Theory, unpublished (1995)Google Scholar
  12. 12.
    L.I. Schiff, Quantum Mechanics (McGraw-Hill, Inc., New York, 1968)Google Scholar
  13. 13.
    David J. Griffiths, Introduction to Quantum Mechanics (Prentice Hall, Inc., New Jersey, 1995)Google Scholar
  14. 14.
    W. Greiner, Quantum Mechanics: An Introduction (Springer-Verlag, Berlin, 1994)Google Scholar
  15. 15.
    H.A. Bethe, Phys. Rev. 72, 339 (1947) (See Bethe’s treatment of the Lamb shift in ref. SAADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Universidad de ConcepcionDepartamento de FisicaConcepcionChile
  2. 2.Universidad de Los AndesFacultad de Ingeniería y Ciencias AplicadasSantiagoChile

Personalised recommendations