Generalized Quasi-Exactly-Solvable Quanta1 Problems,the Represent at ions and Differential Realization of General Deformation of su(2)

This paper is devoted to building the represen tation theory of the general deformation for su(2) and then using it to generalize the quasi-exactly-solvable quan tal (QESQ) problems. For the finite dimensional and infinite dimensional representations, two classes of generalized QESQ models are respectively constructed in terms of the differential realization of the general deformation of su(2). When the deformation is the q-deformation in the quantum group theory, the QESQ model is discussed in detail by associating it with the nonlinear precession of high spins in an external field.