No abstract

An explicit and computable asymptotic integral representation is obtained for the time-dependent Wigner distribution associated with the initial quantum state ψ(x,0)=f(x) eiS(x)/ℏ in the semiclassical (ℏ→0) limit. The approximations are valid to arbitrarily high order in ℏ over any finite time interval. The leading order term is further analyzed to obtain a classically determined phase space function which is related to a classical probability density on phase space. The results hold for a large class of time-dependent potentials.

No abstract

The 11-+0 limit ofthe quantum dynamics determined by the Hamiltonian H(Il) = -(if 12m) 11 + Von L 2 (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 C ~ the error terms are shown to have L 2 norms of order 11112 -E for arbitrarily small positive E.