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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics