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 at one of the crucial moments of its creation.

Keywords: Schrödinger equation, Klein—Fock—Gordon equation, Dirac equation, hydrogen atom, Sommerfeld fine structure formula, Wentzel—Kramers—Brillouin (WKB) approximation, Laplace transform, Nikiforov—Uvarov method PACS: 01.65.+g, 03.65.−w (all) DOI: 10.3367/UFNe.2021.06.039000 URL: https://ufn.ru/en/articles/2022/1/e/ 000788597000005 2-s2.0-85128558753 2022PhyU...65...90B Citation: Barley K, Vega-Guzmán J, Ruffing A, Suslov S K "Discovery of the relativistic Schrödinger equation" Phys. Usp. 65 90–103 (2022) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 23rd, January 2021, revised: 21st, June 2021, accepted: 30th, June 2021 Оригинал: Барли К, Вега-Гузман Х, Руффин А, Суслов С К «Открытие релятивистского уравнения Шрёдингера» УФН 192 100–114 (2022); DOI: 10.3367/UFNr.2021.06.039000 E. Shrödinger is author of Physics-Uspekhi