content_image/327435.jpg content_image/327437.jpg content_image/327438.jpg content_image/327434.jpg content_image/327436.jpg
walls at z = 0 and z = L . The spectral signature of such z -dependent potential settings is clear, therefore. That is, a quantum particle endowed with a position- dependent-mass M ( ρ, ϕ, z ) = M ( ρ ) = ρ − 2 and subjected to an interaction potential of the form 

with ˜ V ( z ) defined in (25), would admit exact energy eigenvalues given by 

On the other hand, a quantum particle endowed with a position-dependent- mass M ( ρ, ϕ, z ) = M ( ρ ) = ρ − 2 subjected to an interaction potential of the form 

with ˜ V ( z ) defined in (25), would be accompanied by exact energy eigenvalues of the form 

## 3.2 Spectral signatures of a ˜ V ( z ) Morse model 

Consider a Morse type interaction ˜ V ( z ) = D ( e − 2 ϵz − 2 e − $^{ϵz}$) ; D > 0, in (18). We may then closely follow the methodical proposal of Chen [31] to obtain 

where one should consider 2 m = ℏ = 1, a → ϵ , E → K 2 z and x → z of Chen [31] to match our settings in (18). Therefore, a PDM quantum particle endowed 

<img src='content_image/327435.jpg'>

<img src='content_image/327437.jpg'>

<img src='content_image/327438.jpg'>

<img src='content_image/327434.jpg'>

<img src='content_image/327436.jpg'>

