Regularity for eigenfunctions of Schrödinger operators
نویسندگان
چکیده
We prove a regularity result in weighted Sobolev (or Babuška–Kondratiev) spaces for the eigenfunctions of a single-nucleus Schrödinger operator. More precisely, let K a (R ) be the weighted Sobolev space obtained by blowing up the set of singular points of the potential V (x) = ∑ 1≤j≤N bj |xj | + ∑ 1≤i<j≤N cij |xi−xj | , x ∈ R 3N , bj , cij ∈ R. If u ∈ L(R ) satisfies (−∆ + V )u = λu in distribution sense, then u ∈ K a for all m ∈ Z+ and all a ≤ 0. Our result extends to the case when bj and cij 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.
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