with a new class of non-Hermitian P ϕ T $_{ϕ}$-symmetric Hamiltonians (having real spectra identical to their Hermitian partner Hamiltonians), we tried to fill this gap, at least partially. Through our over simplified non-Hermitian P ϕ T $_{ϕ}$-symmetrized Hamiltonian (33), we have shown that some conventional relativistic and non-relativistic quantum mechanical results are indeed recoverable (the energy eigenvalues here). We have witnessed, however, an unavoidable change in the azimuthal part of the general wavefunction. Such a change would introduce some new probabilis- tic interpretations. With V ( θ ) = 0 and V$_{ef f}$ ( ϕ ) = − a $^{2}$e $^{iϕ}$, for example, we have observed that a quantum state becomes more localized as the probability density intensifies at a specific point | ϕ | = 0 (documented in figures 1 and 2 of section 3.1). Moreover, setting V ( θ ) = 0 (again with V$_{ef f}$ ( ϕ ) = − a $^{2}$e iϕ in H$_{ϕ}$ ) in the descendant Hamiltonian H$_{θ}$ has indeed manifested a change in the angular θ -dependent part of the general solution too (documented in section 3.2). This would, of course, has some ”new” effects on the probabilistic inter- pretations in turn. Yet, a recipe to keep the magnetic quantum number m as defined in the regular Hermitian quantum mechanical settings is suggested. In connection with the current proposal’s spherical-separability and non- Hermiticity, it is obvious that the descendant Hamiltonians H$_{r}$ , H$_{θ}$, and H$_{ϕ}$ play essential roles and offer some ”user-friendly”, say, options as to which one (or ones) of them is (or are) non-Hermitian. Be it P ϕ T $_{ϕ}$-symmetric, PT - symmetric, pseudo-Hermitian or η -pseudo-Hermitian, they very well fit into Bender’s and Boettcher’s PTQM (irrespective with their nicknames and with the understanding that P and T need not necessarily identify just parity and time reversal, respectively). Yet, a complexification of 0 = V ( θ ) ∈ C in H$_{θ}$ with the understanding that a parity-like P θ and a time reversal-like T θ oper- ators may very well suggest a similar P θ T $_{θ}$-symmetric H$_{θ}$ Hamiltonian. Such 15