in [3]. Consequently, the ordering ambiguity conflict does not only depend on the heterojunction boundaries and the Dutra and Almeida’s [4] reliability test (cf., e.g., Ref.s [3,4] for more details). The potential and/or the form of the position dependent mass have their say in the process [3]. At the end of the day, however, the consensus is that this ambiguity is mainly attributed to the lack of the Galilean invariance (cf., e.g., Ref.[1] on the details of this issue). In the current methodical proposal, we shall be working with the ambi- guity parameters as they are without any discrimination as to which set of ordering is favorable than which. We discuss the von Roos Hamiltonian (1) using cylindrical coordinates and seek some feasible separability in section 2. Therein, we suggest the position-dependent-mass to be only radial-dependent (i.e., m ( ⃗ r ) = m ◦ M ( ρ, ϕ, z ) = M ( ρ, ϕ, z ) = M ( ρ ) = 1 /ρ $^{2}$) and azimuthal sym- metrization is sought through the assumption that Of course, this constitutes only a one feasible separability of the system (other separability options may occur as well), as justified in section 2. In section 3, within the radial cylindrical settings, we consider two examples of fundamental nature. The radial cylindrical ”Coulombic” ˜ V ( ρ ) = − 2 /ρ and the ”harmonic oscillator” ˜ V ( ρ ) = a $^{2}$ρ$^{2}$/ 4. The spectral signatures of different ˜ V ( z ) settings on the Coulombic and harmonic oscillator spectra are reported for impenetrable walls at z = 0 and z = L , for a Morse [31], for a non-Hermitian PT -symmetrized Scarf II [28,32,33], and for a non-Hermitian PT -symmetrized Samsonov [28,34] interaction models. Where, P denotes parity and T mimics the time reflection (cf., e.g., Ref.[28] and references cited therein on this issue). Our concluding remarks are in section 4. 3 V ( ⃗ r ) = V ( ρ, ϕ, z ) = ρ 2 2 [ ˜ V ( ρ ) + ˜ V ( z ) ] . (2)