content_image/306132.jpg content_image/306126.jpg content_image/306127.jpg content_image/306124.jpg content_image/306125.jpg
with 

and 

Which, in turn, results 

with the auxiliary constraint 

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). 

## 3.2.1 Spectral signatures of some ˜ V ( z ) potentials on the radial Coulom- bic spectrum 

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 

<img src='content_image/306132.jpg'>

Moreover, if this PDM-particle is subjected to move in a Morse type [31] 

<img src='content_image/306126.jpg'>

<img src='content_image/306127.jpg'>

<img src='content_image/306124.jpg'>

<img src='content_image/306125.jpg'>

