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Variational Estimates using a Discrete Variable Representation

M. Lombardi·P. Barletta·A. Kievsky
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Abstract

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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M. Lombardi, P. Barletta, A. Kievsky. 2004-06-29. Variational Estimates using a Discrete Variable Representation. https://doi.org/10.1103/physreva.70.032503

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