Communications in Mathematical Physics

, Volume 255, Issue 1, pp 183–227 | Cite as

Sharp Regularity Results for Coulombic Many-Electron Wave Functions

  • Søren Fournais
  • Maria Hoffmann-Ostenhof
  • Thomas Hoffmann-Ostenhof
  • Thomas Østergaard Sørensen


We show that electronic wave functions ψ of atoms and molecules have a representation ψ= Open image in new window ϕ, where Open image in new window is an explicit universal factor, locally Lipschitz, and independent of the eigenvalue and the solution ψ itself, and ϕ has second derivatives which are locally in L. 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.


Neural Network Statistical Physic Wave Function Complex System Nonlinear Dynamics 
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© The authors 2004

Authors and Affiliations

  • Søren Fournais
    • 1
  • Maria Hoffmann-Ostenhof
    • 2
  • Thomas Hoffmann-Ostenhof
    • 3
    • 4
  • Thomas Østergaard Sørensen
    • 5
  1. 1.CNRS and Laboratoire de Mathématiques, UMR CNRS 8628Université Paris-Sud - Bât 425Orsay CedexFrance
  2. 2.Fakultät für MathematikUniversität WienViennaAustria
  3. 3.The Erwin Schrödinger International Institute for Mathematical PhysicsViennaAustria
  4. 4.Institut für Theoretische ChemieUniversität WienViennaAustria
  5. 5.Mathematisches InstitutUniversität MünchenMunichGermany

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