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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. 

## 2 Separability and preliminaries of Dirac and Schr¨ odinger equations revisited 

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 

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