Analytic structure of many-body Coulombic wave functions
Abstract
We investigate the analytic structure of solutions of non-relativistic Schr"odinger equations describing Coulombic many-particle systems. We prove the following: Let psi(x) with x=(x1,...,xN) in R3N denote an N-electron wavefunction of such a system with one nucleus fixed at the origin. Then in a neighbourhood of a coalescence point, for which x1=0 and the other electron coordinates do not coincide, and differ from 0, psi can be represented locally as psi(x) = psi(1)(x) + |x1|psi(2)(x) with psi(1), psi(2) real analytic. A similar representation holds near two-electron coalescence points. The Kustaanheimo-Stiefel transform and analytic hypoellipticity play an essential role in the proof.
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