Journal of Statistical Physics

, Volume 51, Issue 1–2, pp 205–214 | Cite as

A law of large numbers and a central limit theorem for the Schrödinger operator with zero-range potentials

  • R. Figari
  • H. Holden
  • A. Tetab


We consider the Schrödinger operator with zero-range potentials onN points of three-dimensional space, independently chosen according to a common distributionV(x). Under some assumptions we prove that, whenN goes to infinity, the sequence converges to a Schrödinger operator with an effective potential. The fluctuations around the limit operator are explicitly characterized.

Key words

Zero-range potentials law of large numbers effective potentials 


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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • R. Figari
    • 1
  • H. Holden
    • 2
  • A. Tetab
    • 1
  1. 1.Research Center Bielefeld-Bochum-StochasticsGermany
  2. 2.Institute of MathematicsUniversity of TrondheimTrondheim-NTHNorway

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