Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure

For quantum systems with semi-simple Lie algebraic structures,the exact solutions of the equations of motion are obtained by means of algebraic dynamics.The Hamiltonian is transformed into a linear function of Cartan operators by a set of gauge transformations. The coefficients of the gauge transformations are determined by a set of ordinary differential 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.