03-549 S\{o}ren Fournais, Maria Hoffmann-Ostenhof, Thomas Hoffmann-Ostenhof, Thomas \{O}stergaard S\{o}rensen

Sharp regularity results for many-electron wave functions (144K, LaTex2e) Dec 23, 03

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Abstract. We show that electronic wave functions $\psi$ of atoms and molecules have a representation $\psi=\mathcal F \phi$, where $\mathcal F$ is an explicit universal factor, locally Lipschitz, and independent of the eigenvalue and the solution $\psi$ itself, and $\phi$ has locally bounded second derivatives. This representation turns out to be optimal as can already be demonstrated with the help of hydrogenic wave functions. The proofs of these results are, in an essential way, based on a new elliptic regularity result which is of independent interest. Some identities that can be interpreted as cusp conditions for second order derivatives of $\psi$ are derived.

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