Søren Fournais, Maria Hoffmann-Ostenhof, Thomas Hoffmann-Ostenhof, Thomas Østergaard Sørensen
Sharp Regularity Results for Many-Electron Wave Functions
The paper is published: Commun. Math. Phys., 255 (2005) no. 1, 183-227

MSC:

35B65 Smoothness/regularity of solutions of PDE

35J10 Schrodinger operator, See also {35Pxx}

35B45 A priori estimates

81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and other quantum-mechanical equations

35J15 General theory of second-order, elliptic equations

81V55 Molecular physics, See also {92E10}

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.

Keywords: Elliptic PDE, Schrodinger Operators, Regularity of Solutions