interaction ˜ V ( z ) = D ( e − 2 ϵz − 2 e − $^{ϵz}$) ; D > 0. In this case, and the exact energies are of the form Where ˜ n$_{z}$ = 0 , 1 , 2 , 3 , · · · . Obviously, the condition ( √$_{D/ϵ}$ − ˜ n$_{z}$ − 1 2 ) > 0 is manifested here and ought to be enforced, otherwise complex pairs of energy eigenvalues are obtained in the process. Next, let M ( ρ, ϕ, z ) = M ( ρ ) = bρ − $^{1}$/ 2 move under the influence of a trigonometric Rosen-Morse potential ˜ V ( z ) = U$_{◦}$ cot 2 ( πz/d ) ; z ∈ [0 , d ]. Then, and We have recollected the most relevant and vital relations (equations (2)-(5) above) that have been readily reported by Mustafa [31] for cylindrical coor- dinates separability of the PDM-Hamiltonian in (1), where the PDM-setting was considered in the form M ( ρ, ϕ, z ) = g ( ρ ) f ( ϕ ) k ( z ) = g ( ρ ) = 1 /ρ 2 under azimuthally symmetric settings. In this work, however, we offered a more general power-law radial position- V ( ρ, ϕ, z ) = − ˜ A b + ρ b D ( e − 2 ϵz − 2 e − $^{ϵz}$) ; D > 0 , (38) E = ± 1 ˜ $_{b}$√ √ ( √$_{D}$ ϵ − ˜ n$_{z}$ − 1 2 ) ( n$_{ρ}$ + √ ( m 2 + 3 / 4) − ( ζ − β ) / 2 + 1 ) − ˜ A ˜ b , (39) V ( ρ, ϕ, z ) = − ˜ A b + ρ b U$_{◦}$ cot $^{2}$( πz/d ) ; z ∈ [0 , d ] , (40) E = $_{±}$√ [ Cd + ˜ n$_{z}$π ] 2 − U$_{◦}$d 2 ˜ bd ( n$_{ρ}$ + √ ( m 2 + 3 / 4) − ( ζ − β ) / 2 + 1 ) − ˜ A ˜ b . (41) 4 Concluding remarks 13