  We show that electronic wave functions Psi of atoms and molecules have a
representation Psi=F*phi, where 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.
