Variational estimates using a discrete variable representation

The advantage of using a discrete variable representation (DVR) is that the Hamiltonian of two interacting particles can be constructed in a very simple form. However, the DVR Hamiltonian is approximate and, as a consequence, the results cannot be considered as variational ones. We will show that the variational character of the results can be restored by performing a reduced number of integrals. In practice, for a variational description of the lowest n bound states only n(n+1)∕2 integrals are necessary whereas D(D+1)∕2 integrals are enough for the scattering states (D is the dimension of the S matrix). Applications of the method to the study of dimers of He, Ne and Ar, for both bound and scattering states, are presented.