Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties

We construct generalized coherent states for the rationally extended Scarf-I potential. Statistical and geometrical properties of these states are investigated. Special emphasis is given to the study of spatio-temporal properties of the coherent states via the quantum carpet structure and the auto-correlation function. Through this study, we aim to find the signature of the "rationalization" of the conventional potentials and the classical orthogonal polynomials.