dependent mass recipe M ( ρ, ϕ, z ) = g ( ρ ) = bρ 2 υ $^{+1}$/ 2; υ, b ∈ R , within which M ( ρ, ϕ, z ) = g ( ρ ) = 1 /ρ 2 of [31] represents a special case (the results and ex- amples reported therein hold true and yet document additional examples on the applicability of the current methodical proposal, therefore). Moreover, the structure of the position-dependent energy term bρ 2 υ $^{+1}$f ( ϕ ) k ( z ) E in (11) sug- gests that there are five feasible cases towards separability; (i) f ( ϕ ) = 1 = k ( z ), (ii) k ( z ) = 1 = g ( ρ ), (iii) f ( ϕ ) = 1 = g ( ρ ), (iv) υ = − 3 / 2, k ( z ) = 1, f ( ϕ ) = 1, and (v) υ = − 3 / 2, k ( z ) = 1, f ( ϕ ) = 1 (which would break azimuthal sym- metry, of course). Therefore, the separability of (3) may be facilitated by the forms of the position-dependent mass and the interaction potential V ( ρ, ϕ, z ). These are not the only cases to secure separability of (3), so to speak. We have considered two particular mass settings; a radial harmonic oscil- lator type, M ( ρ, ϕ, z ) = M ( ρ ) = g ( ρ ) = bρ $^{2}$/ 2, and a radial Coulombic type, M ( ρ, ϕ, z ) = M ( ρ ) = g ( ρ ) = bρ − $^{1}$/ 2. We have observed that for the Coulombic case two branches of energies are obtained, each of which is a ”mirror-reflection” of the other about the zero-energy axis. Moreover, when we subjected the radial harmonic oscillator mass to a radial harmonic oscillator potential ˜ V ( ρ ) = a $^{2}$ρ$^{2}$/ 4 and the radial Coulombic mass to a radial Coulombic potential ˜ V ( ρ ) = − 2 ˜ A/ρ , only constant shifts in the energies where observed (i.e., a shift ( a $^{2}$/ 4 b ) for the radial harmonic oscillator mass and ( − ˜ A/ ˜ b ) for the radial Coulombic mass, documented in (20) and (35), respectively). That is, the radial interaction po- tentials ˜ V ( ρ ) considered for the two over simplified examples here provided no quantization recipe at all (i.e., they have only introduced constant shifts to the energies but not discrete quantum energy shifts). This is because the form of the general interaction potential V ( ρ, ϕ, z ) we have adopted in (5). Yet, auxiliary constraints on the ambiguity parameters (see (21) for the harmonic oscillator and (36) for the Coulombic) are observed mandatory to 14