No abstract

We investigate nodal sets of magnetic Schrödinger operators with zero magnetic field, acting on a non simply connected domain in R 2 . For the case of circulation 1/2 of the magnetic vector potential around each hole in the region, we obtain a characterisation of the nodal set, and use this to obtain bounds on the multiplicity of the groundstate. For the case of one hole and a fixed electric potential, we show that the first eigenvalue takes its highest value for circulation 1/2.

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

We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in R 3 away from the nuclei.Date: November 22, 2002.

Abstract. We prove that the electron densities of electronic eigenfunctions of atoms and molecules are smooth away from the nuclei.