Evolution of semiclassical quantum states in phase space

The authors derive a semiclassical formula for the Wigner function W(q,p,t) describing the evolution in the two-dimensional phase space qp of a nonstationary quantum state psi (q,t) for a system with one degree of freedom. The initial state psi (q,0) corresponds to a family of classical orbits represented by a curve C0 in qp. Under the classical motion C0 evolves into a curve Ct; it is shown that the region where W is large hugs Ct in an adiabatic fashion, and that W has semiclassical oscillations depending only on the geometry of Ct and neighbouring curves.