Equivalent non-rational extensions of the harmonic oscillator, their ladder operators and coherent states

TL;DR

This paper introduces a family of non-rational quantum potentials extending the harmonic oscillator, constructs ladder operators, and analyzes their coherent states, revealing non-classical behaviors through various quantum properties.

Contribution

It presents a novel method to generate non-rational extensions of the harmonic oscillator using supersymmetric transformations and constructs associated ladder operators and coherent states.

Findings

Coherent states exhibit non-classical behavior.

Analysis of Wigner functions shows quantum interference effects.

Mean-energy and probability densities reveal unique quantum dynamics.

Abstract

In this work, we generate a family of quantum potentials that are non-rational extensions of the harmonic oscillator. Such a family can be obtained via two different but equivalent supersymmetric transformations. We construct ladder operators for these extensions as the product of the intertwining operators of both transformations. Then, we generate families of Barut-Girardello coherent states and analyze some of their properties as temporal stability, continuity on the label, and completeness relation. Moreover, we calculate mean-energy values, time-dependent probability densities, Wigner functions, and the Mandel Q-parameter to uncover a general non-classical behavior of these states.