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 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 10 3.2 Spectral signatures of a ˜ V ( z ) Morse model K 2 z = ( √$_{D}$ ϵ − ˜ n$_{z}$ − 1 2 ) , ˜ n$_{z}$ = 0 , 1 , 2 , 3 , · · · (32) E$_{n}$$_{ρ}$$_{,m,n}$$_{z}$ = ( m 2 + 3 2 ) − ( ζ − β ) − 1 2 ( n 2 $_{z}$π 2 aL 2 + 2 n$_{ρ}$ + 1 ) 2 . (31) V ( ρ, ϕ, z ) = − 2 ρ + ρ 2 ˜ V ( z ) , (28) E$_{n}$$_{ρ}$$_{,m,n}$$_{z}$ = ( m 2 + 3 2 ) − ( ζ − β ) − 1 2 ( L n$_{z}$π − n$_{ρ}$ − 1 ) 2 , (29) V ( ρ, ϕ, z ) = a $^{2}$ρ$^{4}$/ 4 + ρ 2 ˜ V ( z ) , (30)