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arXiv · 0806.1004

Analytic structure of many-body Coulombic wave functions

Søren Fournais·Maria Hoffmann-Ostenhof·Thomas Hoffmann-Ostenhof·Thomas Østergaard Sørensen
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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.

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Søren Fournais, Maria Hoffmann-Ostenhof, Thomas Hoffmann-Ostenhof, Thomas Østergaard Sørensen. 2008-06-05. Analytic structure of many-body Coulombic wave functions. https://doi.org/10.1007/s00220-008-0664-5

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