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Comparison among Klein-Gordon equation, Dirac equation and Relativistic Stationary Schrodinger equation

Guang-jiong Ni·Weimin Zhou·Jun Yan
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Abstract

A particle is always not pure. It always contains hiding antiparticle ingredient which is the essence of special relativity. Accordingly, the Klein-Gordon (KG) equation and Dirac equation are restudied and compared with the Relativistic Stationary Schrödinger Equation (RSSE). When an electron is bound in a Hydrogenlike atom with pointlike nucleus having charge number $Z$, the critical value of $Z, Z_c$, equals to 137 in Dirac equation whereas $Z_c=\sqrt{M/μ} (137)$ in RSSE with $M$ and $μ$ being the total mass of atom and the reduced mass of the electron.

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Guang-jiong Ni, Weimin Zhou, Jun Yan. 2000-02-25. Comparison among Klein-Gordon equation, Dirac equation and Relativistic Stationary Schrodinger equation. https://arxiv.org/abs/quant-ph/9901018

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