使用离散变量表示的变分估计
Variational Estimates using a Discrete Variable Representation
摘要：
使用离散变量表示（DVR）的优点是可以以非常简单的形式构造两个相互作用粒子的哈密顿量。然而，DVR哈密顿量是近似的，因此，结果不能被认为是变分的。我们将表明，结果的变分性质可以通过减少积分次数来恢复。实际上，对于最低n个束缚态的变分描述，仅需要n（n+1）/2个积分，而对于散射态，D（D+1）/2个积分就足够了（D是S矩阵的维数）。应用该方法的研究二聚体的He，Ne和Ar，为束缚态和散射态，提出。
英文摘要：
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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