the semiclassical limit of quantum dynamics. I. time evolution
The ℏ→0 limit of the quantum dynamics determined by the Hamiltonian H(ℏ) =−(ℏ2/2m)Δ+V on L 2(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 ℏ1/2−ε for arbitrarily small positive ε.