  The dynamics of an initially sharp-boundary wavepacket in the presence of an
arbitrary potential barrier are investigated. It is shown that the penetration
through the barrier is universal in the sense that it depends only on the
values of the wavefunction and its derivatives at the boundary. The dependence
on the derivatives vanishes at long distances from the barrier, where the
dynamics are governed solely by the initial value of the wavefunction at the
boundary.
