Nonlinear schrödinger equations and the separation property

Gerald A. Goldin, George Svetlichny

Research output: Contribution to journalArticlepeer-review


We investigate hierarchies of nonlinear Schrödinger equations for multiparticle systems satisfying the separation property, i.e., where product wave functions evolve by the separate evolution of each factor. Such a hierarchy defines a nonlinear derivation on tensor products of the single-particle wave-function space, and satisfies a certain homogeneity property characterized by two new universal physical constants. A canonical construction of hierarchies is derived that allows the introduction, at any particular “threshold” number of particles, of truly new physical effects absent in systems having fewer particles. In particular, if single quantum particles satisfy the usual (linear) Schrödinger equation, a system of two particles can evolve by means of a fairly simple nonlinear Schrödinger equation without violating the separation property. Examples of Galileian-invariant hierarchies are given.

Original languageEnglish (US)
Pages (from-to)120-132
Number of pages13
JournalJournal of Nonlinear Mathematical Physics
Issue number2
StatePublished - Jan 1995

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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