Transient and asymptotic effects in tunneling

The time dependence, from the transient to the stationary regime, of a quantum state initially prepared as a cutoff plane wave impinging on a one-dimensional square barrier is analyzed in detail using a decomposition based on a discrete set of critical points in the complex momentum plane. The motion and shape of the main wave front, the forerunners, and asymptotic (large time) features of the wave are discussed by means of the exact solution and in terms of velocities and characteristic times associated with the partial contributions of the critical points. {} 1996 The American Physical Society.