Husimi's Q-function isotonic oscillator in a generalized negative binomial states representation

TL;DR

This paper explores generalized negative binomial states for the isotonic oscillator, deriving their Husimi's Q-function and demonstrating its application in estimating thermodynamic bounds.

Contribution

It introduces a new class of states for the isotonic oscillator and derives their Husimi's Q-function, linking quantum state properties to thermodynamic estimates.

Findings

Verified properties for generalized negative binomial states as coherent states

Derived Husimi's Q-function for the isotonic oscillator states

Established a lower bound for thermodynamic potential using the Q-function

Abstract

While considering a class of generalized negative binomial states, we verify that the basic minimum properties for these states to be considered as coherent states are satisfied. We particularize them for the case of the Hamiltonian of the isotonic oscillator and we determine the corresponding Husimi's Q-function. This function may be used to determine a lower bound for the thermodynamical potential of the Hamiltonian by applying a Berezin-Lieb inequality