Analytical investigation of revival phenomena in the finite square-well potential

Abstract

We present an analytical investigation of revival phenomena in the finite square-well potential. The classical motion, revival, and super-revival time scales are derived exactly for wave packets excited in the finite well. These time scales exhibit a richer dependence on wave-packet energy and on potential-well depth than has been found in other quantum systems: They explain, for example, the difficulties in exciting wave packets with strong classical features at the bottom of a finite well, or with clearly resolved super-revivals in a shallow well. In the proper regions of validity, the time scales predict the instances of wave-packet reformation extremely accurately. Revivals at the bottom of the well are explored as a ``universal'' limit of the general theory, which offers the clearest connection with the series of fractional and full revivals seen in the dynamics of the infinite square-well potential.