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arXiv · 1502.08007

Reconstruction and location of fractional revivals of coherent state wave-packets for potentials associated with exceptional Xm Jacobi-polynomials

Sid-Ahmed Yahiaoui·Mustapha Bentaiba
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Abstract

Gazeau-Klauder coherent states of the extended trigonometric Scarf potential, underlying the quadratic energy spectrum and associated with Jacobi-type Xm exceptional orthogonal polynomials P(a,b,m) n (x), are constructed. The temporal evolution of wave-packet coherent states are performed by means of an autocorrelation function and the full revival properties are investigated in the usual time-domain analysis. This latter seems to be less useful for describing the fractional revivals due to the complicated nature of coherent wave-packet. Fortunately the autocorrelation function revels a little signature of fractional revivals at the vicinity of quarters of the revival time Trev due to the quadratic energy spectrum and the use of the wavelet-based time-frequency analysis of the autocorrelation function provides an analytical and numerical observation of the fractional revivals at different orders of the system.

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Sid-Ahmed Yahiaoui, Mustapha Bentaiba. 2015-02-27. Reconstruction and location of fractional revivals of coherent state wave-packets for potentials associated with exceptional Xm Jacobi-polynomials. https://arxiv.org/abs/1502.08007

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