content_image/315089.jpg content_image/315091.jpg content_image/315088.jpg content_image/315090.jpg
interaction ˜ V ( z ) = D ( e − 2 ϵz − 2 e − $^{ϵz}$) ; D > 0. In this case, 

and the exact energies are of the form 

<img src='content_image/315089.jpg'>

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 

<img src='content_image/315091.jpg'>

## 4 Concluding remarks 

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- 

<img src='content_image/315088.jpg'>

<img src='content_image/315090.jpg'>

