 08106 S{\o}ren Fournais (University of Aarhus & CNRS), Maria HoffmannOstenhof (Vienna University), Thomas HoffmannOstenhof (Vienna University & ESI), Thomas {\O}stergaard S{\o}rensen (Aalborg University)
 Analytic structure of manybody Coulombic wave functions
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Jun 6, 08

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Abstract. We investigate the analytic structure of solutions of nonrelativistic
Schr"odinger equations describing Coulombic manyparticle systems. We
prove the following: Let psi(x) with x=(x_1,...,x_N) in R^{3N} denote
an Nelectron 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_1psi^(2)(x) with psi^(1), psi^(2) real analytic. A similar
representation holds near twoelectron coalescence points. The
KustaanheimoStiefel transform and analytic hypoellipticity play an
essential role in the proof.
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