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Discovery of the relativistic Schrödinger equationa Department of Applied Mathematics and Statistics, Stony Brook University, New York, New York, USA b Department of Mathematics, Lamar University, 200 Lucas Building, P.O. Box 10047, Beaumont, TX, 77706, USA c Landeshauptstadt München, Referat für Bildung und Sport, Seminar TMG Universität, Drygalski Allee 2, 81477, München, 11794-3600, Germany d School of Mathematical and Statistical Sciences, Arizona State University, P.O. Box 871804, Tempe, AZ, 85287-1804, USA 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.
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