Discovery of the relativistic Schrödinger equation

K. Barley, J. Vega-Guzmán, A. Ruffing, S. K. Suslov

Research output: Contribution to journalArticlepeer-review


We discuss the discovery of the relativistic wave equation for a spin-zero charged particle in the Coulomb field by Erwin Schrödinger (presumably during the Christmas holidays of 1925-1926). However, in this new approach, an essential discrepancy was found with the fine structure formula for energy levels already obtained by Sommerfeld in the framework of the 'old' quantum mechanics. As a result, Schrödinger had to withdraw the original 'relativistically framed' article, a draft of which has never been found, from a journal and start all over with his centennial article on the nonrelativistic stationary Schrödinger equation. Our goal here is to follow the original 'relativistic idea' from a modern mathematical viewpoint and elaborate on why Schrödinger did not publish it. We hope that this consideration will encourage readers to study quantum physics starting from one of the crucial moments of its creation.

Original languageEnglish (US)
Pages (from-to)90-103
Number of pages14
Issue number1
StatePublished - Jan 2022


  • Dirac equation
  • Klein-Fock-Gordon equation
  • Laplace transform
  • Nikiforov-Uvarov method
  • Schrödinger equation
  • Sommerfeld fine structure formula
  • Wentzel-Kramers-Brillouin (WKB) approximation
  • hydrogen atom

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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