Abstract
The time evolution of a coherent state is studied in the limit ℏ→0, for a spinless nonrelativistic quantum system in Euclidean space with smooth bounded time-dependent scalar interaction v(x,t). The lowest-order WKB approximation is derived rigorously, complete with an explicit bound on its L2-norm error over a specified finite time interval. The method is based on a constructive series representation of the classical action, thereby avoiding the need to analyze the behavior of classical trajectories. The amplitude of the initial states considered is neither assumed to be of rapid decrease, nor to depend on ℏ.
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