Constructing Barut-Girardello coherent states for the isotonic oscillator in the DOOT approach

TL;DR

This paper constructs and analyzes Barut-Girardello coherent states for the isotonic oscillator using the DOOT approach, exploring their mathematical properties, physical observables, and thermal behavior.

Contribution

It introduces a novel construction of coherent states for the isotonic oscillator within the DOOT framework and studies their properties and thermal characteristics.

Findings

Coherent states exhibit specific mathematical properties via reproducing kernels.

Expectation values of physical observables are computed within these states.

Thermal behavior and P-representation of the system are characterized.

Abstract

In this work, we study the quantum system of the isotonic oscillator from the perspective of the diagonal operator ordering technique (DOOT). Within this framework, we construct the associated Barut-Girardello and Gazeau-Klauder coherent states. We examine their mathematical properties using reproducing kernels and compute the expectation values of observables that characterize the system and its relevant physical features. Further, we perform the quantization of main classical variables in the complex plane. Then, by exploring the thermal behavior of the physical system in the constructed coherent states, we analyze the properties of mixed states described by a canonical density operator. We also obtain the corresponding Glauber-Sudarshan P-representation.