Regularity for Eigenfunctions of Schrodinger Operators

We prove a regularity result in weighted Sobolev (or Babuka-Kondratiev) spaces for the eigenfunctions of certain Schrodinger-type operators. Our results apply, in particular, to a non-relativistic Schrodinger operator of an N-electron atom in the fixed nucleus approximation. More precisely, let be the weighted Sobolev space obtained by blowing up the set of singular points of the potential , , . If satisfies in distribution sense, then for all and all a a parts per thousand currency sign 0. Our result extends to the case when b (j) and c (ij) are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a < 3/2.