Gauge transformations in quantum mechanics and the unification of nonlinear Schrödinger equations

H. D. Doebner, G. A. Goldin, P. Nattermann

Research output: Contribution to journalArticlepeer-review

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Abstract

Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum theories physically equivalent to linear quantum mechanics through nonlinear gauge transformations. We show that under two physically motivated assumptions, these transformations are uniquely determined: they are exactly the group of time-dependent, nonlinear gauge transformations introduced previously tor a family of nonlinear Schrödinger equations. The general equation in this family, including terms considered by Kostin, by Bialynicki-Birula and Mycielski, and by Doebner and Goldin, with time-dependent coefficients, can be obtained from the linear Schrödinger equation through gauge transformation and a subsequent process we call gauge generalization. We thus unify, on fundamental grounds, a rather diverse set of nonlinear time evolutions in quantum mechanics.

Original languageEnglish (US)
Pages (from-to)49-63
Number of pages15
JournalJournal of Mathematical Physics
Volume40
Issue number1
DOIs
StatePublished - Jan 1999

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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