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The semiclassical limit of quantum dynamics. I: Time evolution. (English) Zbl 0647.46060
The $$\hslash \to 0$$ limit of the quantum dynamics determined by the Hamiltonian $$H(\hslash)=-(\hslash^ 2/2m)\Delta +V$$ on $$L^ 2({\mathbb{R}}^ n)$$ is studied for a large class of potentials. By convolving with certain Gaussian states, classically determined asymptotic behavior of the quantum evolution of states of compact support is obtained. For initial states of class $$C^ 1_ 0$$ the error terms are shown to have $$L^ 2$$ norms of order $$\hslash^{-\epsilon}$$ for arbitrarily small positive $$\epsilon$$.

##### MSC:
 46N99 Miscellaneous applications of functional analysis 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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##### References:
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