where ˜ V ( ϕ ) = 0. Such a combination is not a unique one and some other sep- arability settings could be sought. However, we have chosen to stick with the above mentioned combination for it leads into a handy though rather construc- tive separable system of the one-dimensional Schr¨ odinger equations (15), (18), and (19). Assuming azimuthal symmetrization of the problem at hand and within the radial settings, we consider two examples of fundamental nature. The radial cylindrical Coulombic ˜ V ( ρ ) = − 2 /ρ and the radial cylindrical harmonic oscilla- tor ˜ V ( ρ ) = a $^{2}$ρ$^{2}$/ 4. They are indeed exactly solvable within the settings of (21) and admit exact energy eigenvalues documented in (23) and (24), respectively. Nevertheless, the appearance of K$_{z}$ and K 2 z in (23) and (24), respectively, of- fered an opportunity to study their spectral signatures mandated by different ˜ V ( z ) interaction models. Namely, the spectral signatures of ˜ V ( z ) for impen- etrable walls at z = 0 and z = L (27), for a Morse (32), for a non-Hermitian PT -symmetrized Scarf II (38), and for a non-Hermitian PT -symmetrized Sam- sonov [28,34] (43) are reported. To summarize, we have assumed azimuthal symmetry and used the radial cylindrical Coulomb and harmonic oscillator to obtain exact eigenvalues for a new set of interaction potentials (represented in their general form in (2) and detailed in (28), (30), (33), (35), (39), (40), (44), and (46)). In fact, under such azimuthal symmetrization and ˜ V ( z ) setting, this set of exactly-solvable models may grow up as long as one can find exactly-solvable radially cylindrical models (hereby, exact-solvability may even include numerically exactly-solvable models as well). The recipe as how to collect the energy eigenvalues is clear in the above methodical proposal. Acknowledgement 1 I would like to thank both referees for their valuable comments and suggestions. 14