Abstract
The exact solution and the invariant Cartan operator of the linear nonautono-mous system with hw(4) dynamical group which discribes the interaction of a quantized radiation field with a time-dependent classical current are obtained by using the method of algebraic dynamics. The solution is expressed in the bases of both harmonic oscillator state and coherent state. The rule for direct quantum-classical correspondence of the solutions has been established. It has also been shown that the algebraic dynamics might be generalized from the linear dynamic system with a semi-simple Lie algebra to that with a general Lie algebra.
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