We describe the time evolution of a wave function in the infinite square well using a fractional revival formalism and show that at all times the wave function can be described as a superposition of translated copies of the initial wave function. Using the model of a wave form propagating on a dispersionless string from classical mechanics to describe these translations, we connect the reflection symmetry of the square-well potential to a reflection symmetry in the locations of these translated copies, and show that they occur in a ''parity-conserving'' form. The relative phases of the translated copies are shown to depend quadratically on the translation distance along the classical path. We conclude that the time-evolved wave functions in the infinite square well can be described in terms of translations of the initial wave-function shape, without approximation and without any reference to its energy eigenstate expansion. That is, the set of translated initial wave functions forms a Hilbert space basis for the time-evolved wave functions. ͓S1050-2947͑97͒06606-7͔

An image-based wavefront sensing and control algorithm for the James Webb Space Telescope (JWST) is presented. The algorithm heritage is discussed in addition to implications for algorithm performance dictated by NASA's Technology Readiness Level (TRL) 6. The algorithm uses feedback through an adaptive diversity function to avoid the need for phase-unwrapping post-processing steps. Algorithm results are demonstrated using JWST Testbed Telescope (TBT) commissioning data and the accuracy is assessed by comparison with interferometer results on a multi-wave phase aberration. Strategies for minimizing aliasing artifacts in the recovered phase are presented and orthogonal basis functions are implemented for representing wavefronts in irregular hexagonal apertures. Algorithm implementation on a parallel cluster of high-speed digital signal processors (DSPs) is also discussed.

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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.

We develop a series solution for the bound-state energy levels of the quantum-mechanical one-dimensional finite square-well potential. We show that this general solution is useful for local approximations of the energy spectrum ͑which target a particular energy range of the potential well for high accuracy͒, for global approximations of the energy spectrum ͑which provide analytic expressions of reasonable accuracy for the entire range of bound states͒, and for numerical methods. This solution also provides an analytic description of dynamical phenomena; with it, we compute the time scales of classical motion, revivals, and super-revivals for wave-packet states excited in the well.