with a missing state n$_{z}$ = 2 (the reader may refer to Samsonov [34] on more details on this missing state). Hence, for a PDM quantum particle endowed with M ( ρ, ϕ, z ) = M ( ρ ) = ρ − 2 and subjected to an interaction potential of the form the exact energy eigenvalues would read Whereas, for the exact energy eigenvalues would read where ˜ n$_{z}$ = 1 , 3 , 4 , · · · . The kinetic energy operator in the PDM Hamiltonian (1) is a problem with many aspects that are yet to be explored. In the current work, we tried to study this problem within the context of cylindrical coordinates ( ρ, ϕ, z ). In due course, the essentials related with the kinetic energy operator in (1) are reported. The separability of the Schr¨ odinger equation is sought through a radial cylindrical position dependent mass M ( ρ, ϕ, z ) = M ( ρ ) = 1 /ρ 2 accompanied by an az- imuthally symmetrized interaction potential V ( ρ, ϕ, z ) = ρ 2 [ ˜ V ( ρ ) + ˜ V ( z ) ] / 2, 13 4 Concluding remarks V ( ρ, ϕ, z ) = − 2 ρ − 1 cos z + 2 i sin z ; z ∈ [ − π, π ] , (44) E$_{n}$$_{ρ}$$_{,m,n}$$_{z}$ = ( m 2 + 3 2 ) − ( ζ − β ) − 1 2 ( 2 n$_{z}$ − n$_{ρ}$ − 1 ) 2 . (45) V ( ρ, ϕ, z ) = a $^{2}$ρ$^{4}$/ 4 − 1 cos z + 2 i sin z ; z ∈ [ − π, π ] , (46) E$_{n}$$_{ρ}$$_{,m,n}$$_{z}$ = ( m 2 + 3 2 ) − ( ζ − β ) − 1 2 ( n 2 z 4 a + 2 n$_{ρ}$ + 1 ) 2 . (47)