WIGNERS FUNCTION AND TUNNELING

We construct Wigner's functions of a system with the potential- 1 2ω2q2 to exhibit and resolve some paradoxical features present in this description. Among others, we show that tunneling at negative energies arises through real trajectories associated with positive energies, in contradistinction of the usual WKB picture where this effect comes about by using complex trajectories of the correct energy. We resolve this puzzle by showing (a) that the initial data of this quantal description already contain "wrong" energy regions, (b) the interference phenomenon of WKB wave functions which provides the main contribution to Wigner's function in the semiclassical domain becomes strongly non-local in the presence of a separatrix, which not only allows, but necessitates the presence of these "wrong" classical trajectories in the present description. © 1990.