变分三体问题中基函数的逼近性质
Approximation properties of basis functions in variational three-body problem
摘要：
提出了一种新的具有良好局部逼近性质和多重输出的库仑系统变分基。试函数在所有库仑中心都有适当的行为。非线性渐近参数的引入是温和的：它们不会破坏波函数在粒子间距离消失时的自优化局部行为。有限希尔伯特子空间上的哈密顿量的对角化给出了许多有意义的特征值。因此，与基态一起，一些激发态也被可靠地近似。对于三体系统，所有矩阵元素都可以解析地得到渐近参数的有理函数。计算机代数计算证明了新基使用的可行性。揭示了电子对在库仑中心处的局域能量为负。PACS编号：31.15.Pf
英文摘要：
A new variational basis with well-behaved local approximation properties and multiple output is proposed for Coulomb systems. The trial function has proper behaviour at all Coulomb centres. Nonlinear asymptotic parameters are introduced softly: they do not destroy the self-optimized local behaviour of the wave function at vanishing interparticle distances. The diagonalization of the Hamiltonian on a finite Hilbert subspace gives a number of meaningful eigenvalues. Thus together with the ground state some excited states are also reliably approximated. For three-body systems all matrix elements are analytically obtainable up to rational functions of asymptotic parameters. The feasibility of the new basis usage has been proved by a pilot computer algebra calculation. The negative sign of an electron pair local energy at their Coulomb centre has been revealed. PACS number: 31.15.Pf
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