The semiclassical limit of quantum dynamics. I. Time evolution
Robinson, Sam Leslie
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The ℏ→0 limit of the quantum dynamics determined by the Hamiltonian H(ℏ) =−(ℏ2/2m)Δ+V on L2(Rn) 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 C1/0 the error terms are shown to have L2 norms of order ℏ1/2−ε for arbitrarily small positive ε.