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would admit exact energy eigenvalues given by 

Now, let M ( ρ, ϕ, z ) = M ( ρ ) = bρ $^{2}$/ 2 move under the influence of a trigono- metric Rosen-Morse potential ˜ V ( z ) = U$_{◦}$ cot $^{2}$( πz/d ) ; z ∈ [0 , d ]. Where U$_{◦}$ and d are two positive parameters. In this case, 

(see Ma et al [32] for more details, notice that one should consider 2 µ = ℏ = 1 of Ma as proper parametric mapping into our settings) and 

## 3.2 The Radial Coulombic g ( ρ ) = bρ − $^{1}$/ 2 

Now consider the PDM-particle to have a radial Coulombic-type mass of the form M ( ρ, ϕ, z ) = M ( ρ ) = bρ − $^{1}$/ 2, (i.e., υ = − 1) and subjected to move in a radial Coulombic potential ˜ V ( ρ ) = − 2 ˜ A/ρ . In this case, 

and equation (14) yields 

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