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Aalborg Universitet Analytic structure of solutions to multiconfiguration equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Fournais, Søren Hoffmann-Ostenhof Østergaard, Thomas |
| Copyright Year | 2008 |
| Abstract | We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree–Fock) of Coulomb systems. We prove the following: Let {φ1, . . . , φM} be any solution to the rank–M multiconfiguration equations for a molecule with L fixed nuclei at R1, . . . , RL ∈ R. Then, for any j ∈ {1, . . . , M}, k ∈ {1, . . . , L}, there exists a neighbourhood Uj,k ⊆ R of Rk, and functions φ (1) j,k , φ (2) j,k, real analytic in Uj,k, such that φj(x) = φ (1) j,k(x) + |x−Rk|φ j,k(x) , x ∈ Uj,k . A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo–Stiefel transformation, as applied in [9] to the study of the eigenfunctions of the Schrödinger operator of atoms and molecules near two-particle coalescence points. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://vbn.aau.dk/files/16319628/R-2008-20.pdf |
| Alternate Webpage(s) | https://vbn.aau.dk/ws/portalfiles/portal/16319628/R-2008-20.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
