Deciphering the coalescence behavior of Coulomb-Schrödinger atomic wave functions from an operator product expansion

Abstract

We revisit the coalescence behavior of the atomic Schrödinger wave functions from the angle of an operator product expansion (OPE) within the nonrelativistic Coulomb-Schrödinger effective field theory. We take the electron-nucleus coalescence as an explicit example to demonstrate our formalism, where the celebrated Kato's cusp condition can be easily reproduced. An exact OPE relation is rigorously proved to all orders in perturbation theory. Our approach can be readily extended to ascertain the multi-particle coalescence behaviors of atomic wave functions, as well as to take relativistic effects into account.

v3: 10 pages, 4 figures. Typos corrected, text refined; updated to match the published version