Abstract
Algebraic dynamics and time-dependent dynamical symmetry are proposed. It is proved that every linear nonautonomous system with a semi-simple Lie algebra possesses a time-dependent dynamical symmetry. A gauge transformation is employed for solving the Schrödinger equation of a nonautonomous system with time-dependent dynamical symmetry. The characteristics of the solution and the dynamical diabatic basis are exploited. For linear systems, a remarkable quantum-classical correspondence is found. Quantum motion in a Paul trap serves as an illustration.
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