Abstract

We zoom in on special instances of recently found eigenfunctions for the hyperbolic quantum Calogero–Moser–Sutherland n-particle system in a Morse potential. First, dual difference equations in the spectral variable are employed in order to infer that at the discrete spectrum the pertinent eigenfunctions reduce to previously known ones constructed in terms of multivariate Bessel polynomials. Next, it is confirmed that the celebrated multivariate hypergeometric eigenfunctions of the unperturbed hyperbolic Calogero–Moser–Sutherland model are recovered when the Morse potential is switched off.