Husimi's Q-Function of the Isotonic Oscillator in a Generalized Negative Binomial States Representation

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 is then exploited to obtain a lower bound for the thermodynamical potential of the Hamiltonian by applying a Berezin-Lieb inequality.