Generalized Zernike or disc polynomials: An application in quantum optics

An application of the “generalized Zernike or disc polynomials”, recently introduced in the literature, is shown, resorting to the Lie algebra based investigation of the dynamics of quantum systems driven by two-mode interaction Hamiltonians. Further properties of the associated “disc functions” are deduced. Also, a generalization of the disc polynomials towards the Hahn polynomials is suggested.