  In order to characterize quantum states within the context of information
geometry, we propose a generalization of the Gaussian model, which we called
the Hermite-Gaussian model. We obtain the Fisher-Rao metric and the scalar
curvature for this model, and we show its relation with the one-dimensional
quantum harmonic oscillator. Moreover, using this model we characterize some
failies of states of the quantum harmonic oscillator. We find that for the
eigenstates of the Hamiltonian, mixtures of eigenstates and even or odd
superpositions of eienstates the associated Fisher-Rao metrics are diagonal.
