2010•arXiv (Cornell University)Open access

Exact Solution of the Klein-Gordon Equation for the Hydrogen Atom\n Including Electron Spin

R. Ducharme

Abstract

The term describing the coupling between total angular momentum and\nenergy-momentum in the hydrogen atom is isolated from the radial Dirac equation\nand used to replace the corresponding orbital angular momentum coupling term in\nthe radial K-G equation. The resulting spin-corrected K-G equation is a second\norder differential equation that contains no matrices. It is solved here to\ngenerate the same energy eigenvalues for the hydrogen atom as the Dirac\nequation.\n

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Key concepts: Hydrogen atom, Dirac equation, Hydrogen-like atom, Physics, Angular momentum, Two-body Dirac equations, Angular momentum coupling, Spin (aerodynamics)