Inconsistencies in the description of a quantum system with a finite number of bound states by a compact dynamical group

In a recent paper (Aldaya V and Guerrero J 2005 J. Phys. A: Math. Gen. 38 6939) it is shown that the bound states of the Modified Poschl-Teller potential should be described by the non-compact dynamical group SU(1, 1) instead of the usual compact group SU(2). Here we prove that SU(2) cannot be the dynamical group for a potential with a finite number of bound states on the basis of the Modified Poschl-Teller potential and the Morse potential. This suggests that a quantum system with a continuum spectrum and a finite number of bound states should be described, both in the continuum and the discrete spectrum, by a non-compact dynamical group instead of a compact one.