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Analytic structure of many-body Coulombic wave functions

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  • Søren Fournais
  • Maria Hoffmann-Ostenhof, Universitaet Wien, Austria
  • Thomas Hoffmann-Ostenhof, Universitaet Wien, Austria
  • Thomas Østergaard Sørensen, Denmark
  • Department of Mathematical Sciences
  • Center for Teoretisk Naturvidenskab
We investigate the analytic structure of solutions of non-relativistic Schrödinger equations describing Coulombic many-particle systems. We prove the following: Let ψ(x) with $${{\bf x} = (x_{1},\dots, x_{N})\in \mathbb {R}^{3N}}$$ 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, ψ can be represented locally as ψ(x) = ψ (1)(x) + |x 1|ψ (2)(x) with ψ (1), ψ (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.
Original languageEnglish
JournalCommunications in Mathematical Physics
Volume289
Issue1
Pages (from-to)291-310
Number of pages20
ISSN0010-3616
DOIs
Publication statusPublished - 2009

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