超球调和函数的替代集：通过标架变换满足尖点条件
Alternative sets of hyperspherical harmonics: Satisfying cusp conditions through frame transformations
摘要：
通过扩展欧拉角旋转的概念到三维以上，我们发展了一组新的超球谐函数在高维空间旋转下的系统学。应用这种形式主义，我们确定所有成对的库仑相互作用在一个少体系统，而不求助于多极展开。我们的方法结合了相对坐标与超球面描述的优点。在本方法中，每个库仑矩阵元简化为二体问题中常见的“1/r”形式。因此，我们的计算考虑了当粒子间分离消失时波函数中的所有尖点。与截断多极展开不同，这里给出的计算是精确的。系统的发展过程中的任意数量的粒子，我们证明它明确与最简单的非平凡的例子，三体系统。
英文摘要：
By extending the concept of Euler-angle rotations to more than three dimensions, we develop the systematics under rotations in higher-dimensional space for a novel set of hyperspherical harmonics. Applying this formalism, we determine all pairwise Coulomb interactions in a few-body system without recourse to multipole expansions. Our approach combines the advantages of relative coordinates with those of the hyperspherical description. In the present method, each Coulomb matrix element reduces to the ``1/r'' form familiar from the two-body problem. Consequently, our calculation accounts for all the cusps in the wave function whenever an interparticle separation vanishes. Unlike a truncated multipole expansion, the calculation presented here is exact. Following the systematic development of the procedure for an arbitrary number of particles, we demonstrate it explicitly with the simplest nontrivial example, the three-body system.
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