generating functions is provided to keep the magnetic quantum number as is, whenever deemed necessary of course. In the process of preserving the magnetic quantum number m , a set of isospectral ϕ -dependent potentials, V ( ϕ ), for each set of V ( r ) and V ( θ ) is obtained. This would, moreover, allow reproduction of the conventional-Hermitian relativistic and non-relativistic quantum mechani- cal eigenvalues within our P ϕ T $_{ϕ}$-symmetric non-Hermitian settings. We give our concluding remarks in section 5. Dirac equation with scalar and vector potentials, S ( r ) and V ( r ), respectively, reads (in ℏ = c = 1 units) where and σ is the vector Pauli spin matrix. A Pauli-Dirac representation would, with yield the decoupled equations 2 Separability and preliminaries of Dirac and Schr¨ odinger equations revisited { α · p + β [ M + S ( r )] + V ( r ) } ψ ( r ) = Eψ ( r ) , (6) p = − i ∇ , α =    0 σ σ 0    , β =    I 0 0 − I    , (7) ψ ( r ) =    χ$_{1}$ ( r ) χ$_{2}$ ( r )    , (8) ( σ · p ) χ$_{2}$ ( r ) = [ E − V ( r ) − M − S ( r )] χ$_{1}$ ( r ) , (9) ( σ · p ) χ$_{1}$ ( r ) = [ E − V ( r ) + M + S ( r )] χ$_{2}$ ( r ) . (10) 5