Sharp Regularity Results for Coulombic Many-Electron Wave Functions

We show that electronic wave functions ψ of atoms and molecules have a representation ψ=ϕ, where is an explicit universal factor, locally Lipschitz, and independent of the eigenvalue and the solution ψ itself, and ϕ has second derivatives which are locally in L∞. 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 ψ are derived.

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