Regularity for Eigenfunctions of Schrödinger Operators

Bernd Ammann, Catarina Carvalho, Victor Nistor

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

We prove a regularity result in weighted Sobolev (or Babuška-Kondratiev) spaces for the eigenfunctions of certain Schrödinger-type operators. Our results apply, in particular, to a non-relativistic Schrödinger operator of an N-electron atom in the fixed nucleus approximation. More precisely, let K m a(ℝ 3N, r S) be the weighted Sobolev space obtained by blowing up the set of singular points of the potential, satisfies (-Δ+V)u=λu in distribution sense, then u ∈K m a for all m∈ℤ + and all a ≤ 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.

Original languageEnglish (US)
Pages (from-to)49-84
Number of pages36
JournalLetters in Mathematical Physics
Volume101
Issue number1
DOIs
StatePublished - Jul 2012

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'Regularity for Eigenfunctions of Schrödinger Operators'. Together they form a unique fingerprint.

  • Cite this