Coherent states for rational extensions and ladder operators related to infinite-dimensional representations

The systems we consider are rational extensions of the harmonic oscillator, the truncated oscillator and the radial oscillator. The wavefunctions for the extended states involve exceptional Hermite polynomials for the oscillator and truncated oscillator and exceptional Laguerre polynomials for the radial oscillator. In all cases it is possible to construct ladder operators that have infinite-dimensional representations of their polynomial Heisenberg algebras and couple all levels of the systems. We construct Barut-Girardello coherent states in all cases, eigenvectors of the respective annihilation operators with complex eigenvalues. Then we calculate their physical properties to look for classical or non-classical behaviour.