and satisfies the single-valuedness condition Φ ( ϕ ) = Φ ( ϕ + 2 π ) with C$_{m,a}$ as the normalization constant to be found through the relation Hereby, we have used the fact that our Φ$_{m}$ ( ϕ ) in (34) is P ϕ T $_{ϕ}$-symmetric sat- isfying P ϕ T $_{ϕ}$Φ$_{m}$ ( ϕ ) = Φ$_{m}$ ( ϕ ). This would, in effect, suggest that since R ∋ m = 0 , ± 1 , ± 2 , · · · and H$_{θ}$ of (20) is therefore Hermitian, then H$_{θ}$ of (20) admits real eigenvalues represented by Λ ∈ R . Some illustrative consequences (with H$_{θ}$ of (20) kept Hermitian) are in order. Should V ( θ ) = 0, one may clearly observe that equation (20) is the very well known associated Legendre equation in which Λ = ℓ ( ℓ + 1), where ℓ is the angular momentum quantum number, and Θ ( θ ) = P m ℓ (cos θ ) are the associated Legendre functions. Hence, following the regular textbook procedure one may, in a straightforward manner, show that ℓ ⩾ | m | (i.e., m = 0 , ± 1 , ± 2 , · · · , ± ℓ , is the regular magnetic quantum number). Consequently, as long as the Hermitian radial equation (19) is solvable (could be exactly-, quasi-exactly-, conditionally-exactly-solvable, etc) for the radial interaction V$_{eff}$ ( r ), the spectrum remains invariant and real. However, the global wavefunction (with n$_{r}$ = 0 , 1 , 2 , · · · as the radial quantum number) would indulge some new χ$_{1}$ ( r, θ, ϕ ) = ψ$_{Sch}$ ( r, θ, ϕ ) = √ (2 l + 1) ( l − | m | )! 2 ( l + | m | )! C$_{ma}$R$_{n}$ r $_{l}$( r ) P m l (cos θ ) I$_{2}$$_{m}$ ( 2 ae iϕ/ 2 ) , (36) 1 = 〈 Φ$_{m}$ ( ϕ ) / P ϕ T $_{ϕ}$Φ$_{m}$ ( ϕ ) 〉 = | C$_{m,a}$ | 2 ∫ 2 π 0 ∣ I$_{2}$$_{m}$ ( 2 ae iϕ/ 2 )∣ ∣ ∣$^{2}$ dϕ. (35) 3.1 Consequences of V ( θ ) = 0 in (23) 10