  We construct the system of generalized coherent states for the quantum Kepler
problem corresponds to the homogeneous domain $SU(2,2)/S(U(2)\times U(2))$. We
show that the SU(2,2)-equivariant momentum map for this domain yields the
momentum map for the classical Kepler problem via appropriate limiting passage.
  We also show that under this passage the average values of quantum
observables in this system of coherent states pass into the functions on
classical phase space and $-i/h$ times commutator pass into the Poisson
bracket.
