EXACT-SOLUTIONS OF NONAUTONOMOUS QUANTUM- SYSTEMS WITH SEMISIMPLE LIEALGEBRAIC STRUCTURE

For quantum systems with semi-simple Lie algebraic structures, the exa ct solutions of the equations of motion are obtained by means of algeb raic dynamics. The Hamiltonian is transformed into a linear function o f Cartan operators by a set of gauge transformations. The coefficients of the gauge transformations are determined by a set of ordinary diff erential equations. From the inverses of these gauge transformations, the solutions of the Schrodinger equation, as well as a set of dynamic constants of motion (dynamic invariant operators) are obtained. An SU (3) model serves as an example.