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

Unheeded pseudo solution of Dirac-Coulomb equations with an indirect transformation of functions