Abstract
The formulation of the Dirac equation withelectromagnetic field for a general space–time isspecialized to the Robertson–Walker metric. For aclass of physically meaningful electromagneticpotentials the angular part of the wave function separates asin the free-field case. The scheme is explicitly studiedfor a Coulomb potential. By using a realisticapproximation method one recovers the discrete energy levels of the hydrogen atom in Minkowski space.In case of static space–time, the result is exactfor zero curvature, while it is approximate for nonzerocurvature. The very good order of accuracy of the result is established by a comparison withsimilar qualitative and perturbative results.
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Zecca, A. Dirac Equation with Central Potential: Discrete Spectrum of the Hydrogen Atom in the Robertson–Walker Space–Time. International Journal of Theoretical Physics 38, 945–954 (1999). https://doi.org/10.1023/A:1026677523439
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DOI: https://doi.org/10.1023/A:1026677523439