Properties of nonlinear Schrodinger equations associated with diffeomorphism group representations

H. D. Doebner, G. A. Goldin

Research output: Contribution to journalArticle

79 Scopus citations


The authors recently derived a family of nonlinear Schrodinger equations on R3 from fundamental considerations of generalized symmetry: ih(cross) delta t psi =-(h(cross)2/2m) Del 2 psi +F( psi , psi ) psi +ih(cross)D( Del 2 psi +( mod Del psi mod 2/ mod psi mod 2) psi ), where F is an arbitrary real functional and D a real, continuous quantum number. These equations, descriptive of a quantum mechanical current that includes a diffusive term, correspond to unitary representations of the group Diff(M) parametrized by D, where M=R 3 is the physical space. In the present paper we explore the most natural ansatz for F, which is labelled by five real coefficients. We discuss the invariance properties, describe the stationary states and some non-stationary solutions, and determine the extra, dissipative terms that occur in the Ehrenfest theorem. We identify an interesting, Galilean-invariant subfamily whose properties we investigate, including the case where the dissipative terms vanish.

Original languageEnglish (US)
Article number036
Pages (from-to)1771-1780
Number of pages10
JournalJournal of Physics A: Mathematical and General
Issue number5
StatePublished - Dec 1 1994

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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