Abstract
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.
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