equation) where k = 0 , 1 , 2 , · · · is a ”new” quantum number, and On the other hand, V ( θ ) = 1 / ( 2 cos 2 θ ) would (taking α = β = 0 and γ = 1 in equation (13) of ref.[12) for Dirac equation) result in and For Schr¨ odinger case, nevertheless, one may just replace the term ( E + M ) by (1 / 2) in the above expressions and get the corresponding eigenvalue results. Then the general solution for both cases would read where N$_{n}$ r ,k,m is the normalization constant that can be obtained in a straight- forward textbook procedure. Hereby, we witness that the general solution (44) 12 Θ ( θ ) = y $^{ρ}$(1 − y ) υ $_{2}$F$_{1}$ ( − k, b ; d ; y ) ; y = cos $^{2}$( θ/ 2) , (38) υ = ρ = 1 2 √ m 2 + E + M ; b = k + 4 υ + 1; d = 1 + 2 υ, (39) Λ = 1 4 ( b + k ) 2 − 1 4 = 1 4 [( b + k + 1) ( b + k − 1)] . (40) ρ = 1 4 + 1 4 √ 1 + 4 ( E + M ); υ = 1 2 √ m 2 + E + M (41) b = k + 2 ( ρ + υ ) + 1 2 ; d = 2 ρ + 1 2 (42) Λ = ( b + k ) 2 − 1 4 = [( b + k + 1 2 ) ( b + k − 1 2 )] (43) χ$_{1}$ ( r, θ, ϕ ) = ψ$_{Sch}$ ( r, θ, ϕ ) = N$_{n}$ r $_{,k,m}$R$_{n}$ r $_{,k}$( r ) y $^{ρ}$(1 − y ) υ $_{2}$F$_{1}$ ( − k, b ; d ; y ) I$_{2}$$_{m}$ ( 2 ae iϕ/ 2 ) , (44)