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

TL;DR

This paper constructs Gazeau-Klauder coherent states for an extended trigonometric Scarf potential linked with exceptional Jacobi polynomials, analyzing their revival and fractional revival phenomena using autocorrelation and wavelet-based time-frequency methods.

Contribution

It introduces a novel approach to study fractional revivals of coherent states associated with exceptional orthogonal polynomials using wavelet analysis.

Findings

Autocorrelation function reveals fractional revivals near quarter of the revival time.

Wavelet-based analysis provides detailed observation of fractional revivals.

Full revival properties are confirmed through time-domain analysis.

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.