Accepted articles

From the history of physics


Discovery of the relativistic Schrödinger equation

 a,  b,  c,  d
a 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 1925—1926). However, in this new approach, there was found an essential discrepancy with the fine structure formula for energy levels, already obtained by Sommerfeld in a frame of the 'old' quantum mechanics. As a result, Schrödinger had to withdraw the original 'relativistically framed' article, which draft 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 didn't publish it. We hope that this consideration will encourage the 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, WKB-approximation, Laplace transform, Nikiforov—Uvarov method
DOI: 10.3367/UFNe.2021.06.039000
Citation: Barley K, Vega-Guzmán J, Ruffing A, Suslov S K "Discovery of the relativistic Schrödinger equation" Phys. Usp., accepted

Received: 23rd, January 2021, revised: 21st, June 2021, 30th, June 2021

Оригинал: Барли К, Вега-Гузман Х, Руффин А, Суслов С К «Открытие релятивистского уравнения Шрёдингера » УФН, принята к публикации; DOI: 10.3367/UFNr.2021.06.039000

E. Shrödinger is author of Physics-Uspekhi

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