Quantum Chemistry Research Institute, JST, CREST, Kyodai Katsura Venture Plaza 107, Goryo Oohara 1-36, Nishikyo-ku, Kyoto 615-8245, Japan.
J Chem Phys. 2013 Jul 28;139(4):044114. doi: 10.1063/1.4816281.
We derived the necessary conditions that the non-relativistic time-independent exact wave functions for two-particle systems must satisfy at a coalescence (or cusp) point. Some of such necessary conditions are already known to be Kato's cusp condition (CC) and Rassolov and Chipman's CC. In the present study, we extended and generalized those conditions, calling them generalized coalescence conditions (GCCs). Kato's CC and Rassolov and Chipman's CC were shown to be specific cases included in the GCCs. The GCCs can be applied not only to Coulombic systems but also to any systems where the interaction between two particles is represented in a power series of the inter-particle distance. We confirmed the correctness of our derivation of these GCCs by applying the free complement wave functions of a hydrogen atom in ground and excited states, a harmonic oscillator, and a system with an interacting potential of V = r.
我们推导出了两粒子体系的非相对论时不变精确波函数在合并（或尖点）处必须满足的必要条件。这些必要条件中的一些已经是 Kato 的尖点条件（CC）和 Rassolov 和 Chipman 的 CC。在本研究中，我们扩展和推广了这些条件，称之为广义合并条件（GCC）。Kato 的 CC 和 Rassolov 和 Chipman 的 CC 被证明是 GCC 中包含的特定情况。GCC 不仅可以应用于库仑系统，还可以应用于任何两个粒子之间的相互作用用粒子间距离的幂级数表示的系统。我们通过应用氢原子的基态和激发态、谐振子和相互作用势为 V = r 的系统的自由补全波函数，确认了这些 GCC 的推导的正确性。
