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Motivated by the interface between curved spacetime quantum mechanics and applications in space quantum communications, quantum technologies and quantum optics, the Dirac equation is considered with the recently proposed generalized gravitational interaction (Kepler or Coulomb), which includes post-Newtonian (relativistic) and quantum corrections to the classical potential. The general idea in choosing the metric is that the spacetime contributions are contained in an external potential or in an electromagnetic potential which can be considered as a good basis for future studies on space quantum communication. We also discuss several known generalizations of the Coulomb potential within this formulation in terms of certain Heun functions. The impossibility of solving our equation for the quantum-corrected Coulomb terms using known exact or quasi-exact nonperturbative analytical techniques is discussed, and finally the Bethe-ansatz approach is proposed to overcome this challenging problem.
Baradaran et al. (Tue,) studied this question.