S{\o}ren Fournais (University of Aarhus & CNRS), Maria Hoffmann-Ostenhof (Vienna University), Thomas Hoffmann-Ostenhof (Vienna University & ESI), Thomas {\O}stergaard S{\o}rensen (Aalborg University)
Analytic structure of many-body Coulombic wave functions
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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=(x_1,...,x_N) in R^{3N} 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 
x_1=0 and the other electron coordinates do not coincide, and differ 
from 0, psi can be represented locally as psi(x) = psi^(1)(x) + 
|x_1|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.