ua nt - p h / 99 02 05 8 v 1 1 6 Fe b 19 99 Spin systems , spin coherent states and quasi - exactly solvable models

Spin coherent states play a crucial role in defining QESM (quasi-exactly solvable models) establishing a strict correspondence between energy spectra of spin systems and low-lying quantum states for a particle moving in a potential field of a certain form. Spin coherent states are also used for finding the Wigner-Kirkwood expansion and quantum corrections to energy quantization rules. The closed equation which governs dynamics of a quantum system is obtained in the spin coherent representation directly for observable quantities. Spin coherent states play a crucial role in defining QESM (quasi-exactly solvable models) establishing a strict correspondence between energy spectra of spin systems and low-lying quantum states for a particle moving in a potential field of a certain form. Spin coherent states are also used for finding the Wigner-Kirkwood expansion and quantum corrections to energy quantization rules. The closed equation which governs dynamics of a quantum system is obtained in the spin coherent representation directly for observable quantities. In this paper we review three somewhat unusual applications of spin coherent states: 1) quasi-exactly-solvable models (QESM) and effective potential description of spin systems; 2)dynamics of quantum spin systems in terms of observable quantities; 3) Wigner-Kirkwood expansion and energy quantization rules (analogue of the Bohr-Sommerfeld rules) with quantum corrections, derivation not using the path integral approach; the crucial point here that the series for quantization rules turned out to be the direct consequence of the Wigner