  We analyze the behavior of a quantum system described by a one-dimensional
asymmetric potential consisting of a step plus a harmonic barrier. We solve the
eigenvalue equation by the integral representation method, which allows us to
classify the independent solutions as equivalence classes of homotopic paths in
the complex plane. We then consider the propagation of a wave packet reflected
by the harmonic barrier and obtain an expression for the interaction time as a
function of the peak energy. For high energies we recover the classical
half-period limit.
