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

TL;DR

This paper constructs and analyzes generalized coherent states for the extended Scarf-I potential, exploring their statistical, geometrical, and spatio-temporal properties to understand the effects of potential rationalization.

Contribution

It introduces a new class of coherent states for the rationally extended Scarf-I potential and investigates their unique properties and signatures of potential rationalization.

Findings

Analysis of quantum carpet structures reveals distinctive spatio-temporal patterns.

Auto-correlation functions indicate coherence and revival phenomena.

Statistical properties reflect the influence of potential extension on state behavior.

Abstract

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 `"rationalisation" of the conventional potentials and the classical orthogonal polynomials.