Wave mechanics triumphed when Schrodinger published his now famous equation and showed how to describe Hydrogen-like atoms using it. However, while looking for the right equation, Schrodinger first explored, but did not publish, the equation that we today call the Klein-Gordon equation. An alternative possible choice is explored in this work. It is shown a quasi-relativistic wave equation which solutions match the Schrodinger's results at electron energies much smaller than the energy associated to the electron's mass, but include the relativistic Thomas correction at higher energies. A discussion is presented about several consequences that would follow from using this quasi-relativistic wave equation as a quantum mechanics foundational equation. It is also suggested the academic use of this equation for introducing the students to the implications of the special theory of relativity in introductory quantum mechanics courses.

中文翻译：

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薛定谔还有其他选择吗？

当薛定谔发表了他现在著名的方程并展示了如何使用它描述类氢原子时，波力学取得了胜利。然而，在寻找正确的方程时，薛定谔首先探索了，但没有发表，我们今天称之为克莱因-戈登方程的方程。在这项工作中探索了另一种可能的选择。它显示了一个准相对论波动方程，该方程在电子能量远小于与电子质量相关的能量时与薛定谔的结果相匹配，但包括在更高能量下的相对论 Thomas 校正。讨论了使用这个准相对论波动方程作为量子力学基础方程的几个后果。