Phase-Difference Equations: A Calculus for Quantum Revivals
D. L. Aronstein and C. R. Stroud, Jr.
Laser Physics 15, p. 1496 (2005).
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Equations describing the revival times of multimode quantum systems are transformed into a set of
phase-difference equations, which are discrete difference equations that describe the phase relationships among
the modes of the quantum system at a revival. These equations are developed using an analogy to the differential
equations satisfied by polynomials of a continuous variable and serve as a comprehensive toolkit for investigat-
ing revival phenomena. We apply these equations to two examples in detail to demonstrate their utility, inves-
tigating revivals of selectively populated wavefunctions in the infinite square-well potential and of highly
excited wavepackets in arbitrary one-dimensional potentials.
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Hideomi Nihira ( email@example.com ).
Last modified 13 September 2006