Abstract
The dynamical algebraic structure of a time-dependent $L\ensuremath{-}S$ coupled system is studied. Based on this algebraic structure, the exact solution of the Schr\"odinger equation for the $s=\frac{1}{2}$ case is obtained by using the method of algebraic dynamics. For the $s=1$ case, the SU(3) structure of the time-dependent $L\ensuremath{-}S$ coupled system is also investigated, and it can be solved by the same method.
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