  The generalized coherent states for quantum groups introduced by Jurco and
Stovicek are studied for the simplest example SU_q(2) in full detail. It is
shown that the normalized SU_q(2) coherent states enjoy the property of
completeness, and allow a resolution of the unity. This feature is expected to
play a key role in application of these coherent states in physical models. The
homogeneous space of SU_q(2), i.e. the q-sphere of Podles, is reproduced in
complex coordinates by using the coherent states. Differential calculus in the
complex form on the homogeneous space is developed. High spin limit of the
SU_q(2) coherent states is also discussed.
