Variational Estimates using a Discrete Variable Representation

Details Variational Estimates using a Discrete Variable Representation Variational Estimates using a Discrete Variable Representation

2004-03-11

arxiv.org/abs/physics/0403071v2

Physics

Atomic and Molecular Clusters

30 pages, 7 figures. Minor changes (title modified, typos corrected, 1 reference added). To be published in PRA

Scientific paper

10.1103/PhysRevA.70.032503

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.

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