### 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 language | English (US) |
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Pages (from-to) | 49-84 |

Number of pages | 36 |

Journal | Letters in Mathematical Physics |

Volume | 101 |

Issue number | 1 |

DOIs | |

State | Published - Jul 2012 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Letters in Mathematical Physics*,

*101*(1), 49-84. https://doi.org/10.1007/s11005-012-0551-z