dependent-mass and the interaction potential to take the forms m ( ⃗ r ) ≡ M ( ρ, ϕ, z ) = g ( ρ ) f ( ϕ ) k ( z ) and V ( ⃗ r ) ≡ V ( ρ, ϕ, z ), respectively. We have shown (see Mustafa [31] for more details on this issue) that the corresponding PDM-Schr¨ odinger equation [ H − E ] Ψ ( ρ, ϕ, z ) = 0 with would imply Ψ ( ρ, ϕ, z ) = R ( ρ ) Φ ( ϕ ) Z ( z ) ; ρ ∈ (0 , ∞ ) , ϕ ∈ (0 , 2 π ) , z ∈ ( −∞ , ∞ ) , (2) 0 = 2 g ( ρ ) f ( ϕ ) k ( z ) [ E − V ( ρ, ϕ, z )] + [ R $^{′′}$( ρ ) R ( ρ ) − ( g $^{′}$( ρ ) g ( ρ ) − 1 ρ ) R $^{′}$( ρ ) R ( ρ ) + ζ 2 ( g $^{′}$( ρ ) g ( ρ ) ) 2 − ( β + 1) 2 ( g $^{′}$( ρ ) ρg ( ρ ) + g ′′ ( ρ ) g ( ρ ) )] + [ Z $^{′′}$( z ) Z ( z ) − k $^{′}$( z ) k ( z ) Z $^{′}$( z ) Z ( z ) + ζ 2 ( k $^{′}$( z ) k ( z ) ) 2 − ( β + 1) 2 k ′′ ( z ) k ( z ) ] + 1 ρ 2 [ Φ $^{′′}$( ϕ ) Φ ( ϕ ) − f $^{′}$( ϕ ) f ( ϕ ) Φ $^{′}$( ϕ ) Φ ( ϕ ) + ζ 2 ( f $^{′}$( ϕ ) f ( ϕ ) ) 2 − ( β + 1) 2 f ′′ ( ϕ ) f ( ϕ ) ] (3) ζ = α ( α − 1) + γ ( γ − 1) − β ( β + 1) . (4) 2 M V ( ρ, ϕ, z ) = 2 g ( ρ ) f ( ϕ ) k ( z ) V ( ρ, ϕ, z ) = ˜ V ( ρ ) + ˜ V ( z ) + 1 ρ 2 ˜ V ( ϕ ) . (5) where To facilitate and ease separability, we have suggested that the interaction po- tential satisfies an obviously ”manifested-by-equation (3)” general identity of the form Hereby, we may remind the reader that in [31 } we have used g ( ρ ) = 1 /ρ 2 along with f ( ϕ ) = 1 = k ( z ) as one of the options that secured separability of the problem at hand. 5