with and Which, in turn, results with the auxiliary constraint ∣ ∣$^{˜}$ ℓ$_{−}$ 1 ∣ = √ ( m 2 + 3 / 4) − ( ζ − β ) / 2 , (33) k$_{z}$ = ± ˜ bE + ˜ A ( n$_{ρ}$ + ∣ ∣$^{˜}$ ℓ$_{−}$ 1 ∣ + 1 ) . (34) E = ± k$_{z}$ ˜ b ( n$_{ρ}$ + √ ( m 2 + 3 / 4) − ( ζ − β ) / 2 + 1 ) − ˜ A ˜ b , (35) ( ζ − β ) = α ( α − 1) + γ ( γ − 1) − β ( β + 2) ≤ ( 2 m 2 + 3 / 2 ) , (36) on the ambiguity parameters that secures the reality of E . Nevertheless, two branches of energies are obviously obtained. Moreover, the spectral signature of k$_{z}$ on the overall spectrum is obtained through the solution of equation (13). If we subject our radial Coulombic PDM-particle M ( ρ, ϕ, z ) = M ( ρ ) = bρ − $^{1}$/ 2 to move in V ( ρ, ϕ, z ) = − ˜ A/b + ρ ˜ V ( z ) /b, where ˜ V ( z ) is given by (22), it will admit exact energies of the form Moreover, if this PDM-particle is subjected to move in a Morse type [31] 3.2.1 Spectral signatures of some ˜ V ( z ) potentials on the radial Coulom- bic spectrum E = ± n$_{z}$π ˜ bL ( n$_{ρ}$ + √ ( m 2 + 3 / 4) − ( ζ − β ) / 2 + 1 ) − ˜ A ˜ b ; n$_{z}$ = 1 , 2 , 3 , · · · . (37) 12