Exact solutions of non-autonomous quantum systems with semisimple Lie algebraic structure

Abstract

If a non-autonomous quantum system has an semisimple Lie algebraic structure and its Hamiltonian can be treated as a linear function of the generators of a semisimple Lie group, we show a method for finding a set of gauge transformations that transform the Hamiltonian to a linear function of Cartan operators. The exact solutions of the equations of motion, as well as a set of time-dependent invariant operators which commute with each other, are obtained by the inverse gauge transformations. An SU(3) model serves as an illustration.