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 decompo sition based on a discrete set of critical points in the complex momen tum plane. The motion and shape of the main wave front, the forerunner s, and asymptotic (large time) features of the wave are discussed by m eans of the exact solution and in terms of velocities and characterist ic times associated with the partial contributions of the critical poi nts.