PT-/non-PT-Symmetric and non-Hermitian Hellmann Potential: Approximate Bound and Scattering States with Any $\mathrm{\ell }$-Values

We investigate the approximate bound state solutions of the Schr"odinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained. Numerical values of energy eigenvalues for the bound states are compared with the ones obtained before. Scattering state solutions are also studied. Phase shifts of the potential are written in terms of the angular momentum quantum number $\mathrm{\ell }$.