Phase-Difference Equations: A Calculus for Quantum Revivals

D. L. Aronstein and C. R. Stroud, Jr.

Laser Physics 15, p. 1496 (2005).

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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