Recently we have developed a method to describe approximately the continuum states of a weakly bound system. The method consists on constructing a discrete and normalizable basis by multiplying the ground state of the system by a family of suitable orthogonal polynomials. The Hamiltonian is then diagonalized in the finite basis, giving rise to an accurate description of the excited bound states and to a discretization of the continuum. In this work we present an application of this method to describe the effect of break-up channels in the scattering of deuterons by nuclei. We investigate the case of d + 208Pb at 50 MeV, where the Coulomb force, especially the dipole component, is very important. We also present an application of this method to describe thermodynamic properties associated to the vibration and eventual dissociation of ideal diatomic molecules. We investigate the temperature dependence of the heat capacity per molecule.