Systematic comparison of the quantization rules of hydrogenoid atoms in the Old Quantum, Schrödinger, Klein–Gordon, and Dirac theories, by means of a common set of three parameters

A set of three parameters λ, β, and δ related to energy E and angular momentum L were used to make the closest possible formal comparison between the five successive theories of the quantization of the energy levels of the hydrogenoid atoms. The expression of the quantization rules was made uniform and the differences between the theories were reduced to simple redefinitions of the parameters.