Discovery of the relativistic Schrödinger equation. (1st January 2022)

• Record Type: Journal Article
• Authors: Barley, K; Vega-Guzmán, J; Ruffing, A; Suslov, S K
• Is Part Of: Physics Uspekhi. Volume 65:Number 1(2022)
• Page Start: 90
• Page End: 103
• Publication Date: 2022-01-01
• Subjects: Schrödinger equation -- Klein-Fock-Gordon equation -- Dirac equation -- hydrogen atom -- Sommerfeld fine structure formula -- Wentzel-Kramers-Brillouin (WKB) approximation -- Laplace transform -- Nikiforov-Uvarov method; Physics -- Periodicals; 530.05
• DOI: 10.3367/UFNe.2021.06.039000
• Languages: English
• ISSNs: 1063-7869

Abstract

Abstract: 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.