The conditions on the behavior of a wavefunction for a system of charged particles near the coalescence of any two of them are derived. The new features of the derivation are: (a) the fixedhyphen;nucleus approximation is not required; (b) the wavefunction is not spherically averaged; (c) the wavefunction can have a node at the singularity; and (d) the consequences of the two particles being identical are examined. In addition to the general treatment, the electronmdash;nucleus cusp conditions for diatomic molecules are discussed in detail.
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