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

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 $Z_c=\sqrt{M/\mu }(137)$ in RSSE with $M$ and $\mu$ being the total mass of atom and the reduced mass of the electron.

10 pages, Revtex, 10 Postscript figures