Solutions of Dirac equation for an electron in orbit of an atom are usually expressed in terms of spherical coordinates $r,\theta$ and $\phi$. For a point ($r,\theta,\phi$) the variable $r$ represents the distance from the center of the nucleus. My question is whether this is proper distance or coordinate distance? It may not make a difference in flat space-time but in presence of a gravitational field these two distances may be different. Please quote some reference if possible as I could not find anything mentioned explicitly in literature.
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$\begingroup$ The Dirac equation was formulated to be consistent with Special Relativity, not GR. The only way a gravitational field could have an important effect on the solution is if there are tidal forces on the scale of the electron orbitals; how extreme of a situation are you willing to consider? $\endgroup$– SpencerCommented Oct 12, 2015 at 6:30
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$\begingroup$ @Spencer Dirac equation in GR is a vast field in itself with real implications at atomic level. Search for it and you will find amazing stuff. $\endgroup$– amateurRebelCommented Oct 12, 2015 at 9:51
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