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We revisit the coalescence behavior of the atomic Schr\"odinger wavefunctions from the angle of operator product expansion (OPE) within thenonrelativistic Coulomb-Schr\"odinger effective field theory. We take theelectron-nucleus coalescence as an explicit example to demonstrate ourformalism, where the celebrated Kato's cusp condition can be easily reproduced.An exact OPE relation is rigorously proved to all orders in perturbationtheory. Our approach can be readily extended to ascertain the multi-particlecoalescence behaviors of atomic wave functions, as well as to take relativisticeffects into account.

Deciphering the coalescence behavior of Coulomb-Schr\"odinger atomic wave functions from operator product expansion