Quantum Mechanics of Integrable Spins on Coadjoint Orbits

We investigate classical integrable spins defined on the reduced phase spaces of coadjoint orbits of $G= SU(N)$ and study quantum mechanics of them. After discussions on a complete set of commuting functions on each orbit and construction of integrable spin models on the flag manifolds, we quantize a concrete example of integrable spins on SU(3) flag manifold in the coherent state quantization scheme and solve explicitly the time-dependent Schr\"odinger equation.