  We open out one of incorrect solutions of the Driac equation in the Coulomb
field given in a published paper. By introducing a transformation of function,
the paper transformed the original radial first-order Dirac-Coulomb equation
into two second-order Dirac-Coulomb equation. However, each of the second-order
differential equations has differential energy eigenvalues set. The original
paper wrote the two differential equations into one of forms, and then gave the
distinguished energy eigenvalues. The mathematical procedure is not correct.
For the same quantum system, introducing a transformation of function yields
two different energy eigenvaluse, the result violates the uniqueness of
solution. It actually shows that the given second-order differential equations
have no solution. On the other hand, the given formal solutions of the
second-order Dirac-Coulomb equations violate the conditions for determining
solution. Consequently, the solutions given by the author are pseudo solution,
and the corresponding energy eigenvalues set is also a pseudo eigenvalues set.
