Inventiones mathematicae

, Volume 167, Issue 3, pp 515–614 | Cite as

Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems

  • László Erdős
  • Benjamin Schlein
  • Horng-Tzer YauEmail author


We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schrödinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k.


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • László Erdős
    • 2
  • Benjamin Schlein
    • 1
  • Horng-Tzer Yau
    • 1
    Email author
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Institute of MathematicsUniversity of MunichMunichGermany

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