On the nature of "hidden symmetry" or "accidental degeneracy" in the   Kepler problem
  We propose a symmetry of the Dirac equation under the interchange of signs of eigenvalues of the Dirac's $K$ operator. We show that the only potential which obeys this requirement is the Coulomb one for both vector and scalar cases. 
Tamar T. Khachidze, Anzor A. Khelashvili