  Exact solutions of the Schrodinger and Dirac equations in generalized
cylindrical coordinates of the 3-dimensional space of positive constant
curvature, spherical model, have been obtained. It is shown that all basis
Schrodinger's and Dirac's wave functions are finite, single-valued, and
continuous everywhere in spherical space model S_{3}. The used coordinates
(\rho, \phi,z) are simply referred to Eiler's angle variables (\alpha, \beta,
\gamma), parameters on the unitary group SU(2), which permits to express the
constructed wave solutions \Psi(\rho, phi,z) in terms of Wigner's functions
$D_{mm'}^{j}(\alpha, \beta, \gamma)$. Specification of the analysis to the case
of elliptic, SO(3.R) group space, model has been done. In so doing, the results
substantially depend upon the spin of the particle. In scalar case, the part of
the Schrodinger wave solutions must be excluded by continuity considerations,
remaining functions are continuous everywhere in the elliptical 3-space. The
latter is in agrement with the known statement: the Wigner functions
D_{mm'}^{j}(\alpha, \beta, \gamma) at j =0,1,2,... make up a correct basis in
SO(3.R) group space. For the fermion case, it is shown that no Dirac solutions,
continuous everywhere in elliptical space, do exist. Description of the Dirac
particle in elliptical space of positive constant curvature cannot be correctly
in the sense of continuity adjusted with its topological structure.
