  The eigenvalue problem for radial potentials is considered in a space whose
spatial coordinates satisfy the SU(2) Lie algebra. As the consequence, the
space has a lattice nature and the maximum value of momentum is bounded from
above. The model shows interesting features due to the bound, namely, a
repulsive potential can develop bound-states, or an attractive region may be
forbidden for particles to propagate with higher energies. The exact radial
eigen-functions in momentum space are given by means of the associated
Chebyshev functions. For the radial stepwise potentials the exact energy
condition and the eigen-functions are presented. For a general radial potential
it is shown that the discrete energy spectrum can be obtained in desired
accuracy by means of given forms of continued fractions.
