Klein-Gordon and square-root operator equations for two-spinors and scalars: perturbation calculations for hydrogen-like systems

Details Klein-Gordon and square-root operator equations for two-spinors and scalars: perturbation calculations for hydrogen-like systems Klein-Gordon and square-root operator equations for two-spinors and scalars: perturbation calculations for hydrogen-like systems

2006-02-03

arxiv.org/abs/quant-ph/0602047v1

Physics

Quantum Physics

9 pages

Scientific paper

There exists a Klein-Gordon-like equation for a spin-1/2 particle in an electromagnetic field with 2-spinors as wave functions that is a direct consequence of the corresponding Dirac equation. Thus, it reproduces the same binding energies for an electron in a hydrogen atom as the Dirac equation. There is also a square-root equation for 2-spinors which can give the same binding energies up to the forth order of the fine structure constant, inclusively, what will be shown by means of a comparison of the non-relativistic limit plus a first relativistic correction of both equations for 2-spinors within the framework of a perturbation analysis. A parallel will also be drawn to the spin-0 case.

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