  We analyze the tunneling of a particle through a repulsive potential
resulting from an inverted harmonic oscillator in the quantum mechanical phase
space described by the Wigner function. In particular, we solve the partial
differential equations in phase space determining the Wigner function of an
energy eigenstate of the inverted oscillator. The reflection or transmission
coefficients $R$ or $T$ are then given by the total weight of all classical
phase space trajectories corresponding to energies below, or above the top of
the barrier given by the Wigner function.
