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and 

Where m is the magnetic quantum number and 

is an irrational magnetic quantum number. Hereby, it obvious that the substi- tutions of υ = − 3 / 2 and b = 2 in (14) would inspire a re-scale of the form 

so that our results in [31] for the radial Coulombic ˜ V ( ρ ) = − 2 /ρ and the radial harmonic oscillator ˜ V ( ρ ) = a $^{2}$ρ$^{2}$/ 4 (equations (23) and (24) in [31], respectively) are safely reproduced. Therefore, the corresponding spectral signatures of ˜ V ( z ) interaction potentials for υ = − 3 / 2 and b = 2 (i.e, g ( ρ ) = ρ − $^{2}$) are reported therein [31] and shall not be repeated here. 

## 3 Two particular radial settings; g ( ρ ) = bρ $^{2}$/ 2 and g ( ρ ) = bρ − $^{1}$/ 2 

In this section. we consider the position-dependent mass M ( ρ, ϕ, z ) = g ( ρ ) to indulge a radial harmonic oscillator g ( ρ ) = bρ $^{2}$/ 2 (i.e., υ = 1 / 2) and the radial Coulombic g ( ρ ) = bρ − $^{1}$/ 2 (i.e., υ = − 1) forms. For the sake of keeping this work simple and instructive, we shall consider the radial harmonic oscilla- tor g ( ρ ) = bρ $^{2}$/ 2 accompanied by a radial harmonic oscillator type interaction ˜ V ( ρ ) = a $^{2}$ρ$^{2}$/ 4 and the radial Coulombic g ( ρ ) = bρ − $^{1}$/ 2 accompanied by a radial Coulombic ˜ V ( ρ ) = − 2 ˜ A/ρ . We shall moreover report the spectral signa- 

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