Quantum revivals and carpets in some exactly solvable systems

We consider the revival properties of quantum systems with an eigenspectrum E_{n} proportional to n^{2}, and compare them with the simplest member of this class - the infinite square well. In addition to having perfect revivals at integer multiples of the revival time t_{R}, these systems all enjoy perfect fractional revivals at quarterly intervals of t_{R}. A closer examination of the quantum evolution is performed for the Poeschel-Teller and Rosen-Morse potentials, and comparison is made with the infinite square well using quantum carpets.