08-106 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 (63K, LaTeX2e) Jun 6, 08

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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.

Files: 08-106.src( 08-106.comments , 08-106.keywords , KS-arXiv.tex )