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.

中文翻译：

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相对论薛定谔方程的发现

摘要 我们讨论了欧文·薛定谔（推测在 1925-1926 年圣诞节期间）在库仑场中发现自旋零带电粒子的相对论波动方程。然而，在这种新方法中，发现与 Sommerfeld 在“旧”量子力学框架中已经获得的能级精细结构公式存在本质上的差异。结果，薛定谔不得不从期刊上撤回最初的“相对论框架”文章，其草稿从未被发现，并从他关于非相对论静止薛定谔方程的百年篇文章重新开始。我们的目标是从现代数学的角度遵循最初的“相对论思想”，并详细说明薛定谔没有发表它的原因。