Introducing nonlinear gauge transformations in a family of nonlinear Schrödinger equations

H. D. Doebner, Gerald A. Goldin

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104 Scopus citations

Abstract

In earlier work we proposed a family of nonlinear time-evolution equations for quantum mechanics associated with certain unitary group representations [Doebner and Goldin, Phys. Lett. A 162, 397 (1992); J. Phys. A 27, 1771 (1994)]. Such nonlinear Schrödinger equations are expected to describe irreversible and dissipative quantum systems. Here we introduce and justify physically the group of nonlinear gauge transformations necessary to interpret our equations. We determine the parameters that are actually gauge invariant and describe some of their properties. Our conclusions contradict, at least in part, the view that any nonlinearity in quantum mechanics leads to unphysical predictions. We also show how time-dependent nonlinear gauge transformations connect our equations to those proposed by Kostin [J. Chem. Phys. 57, 3589 (1972)] and by Bialynicki-Birula and Mycielski [Ann. Phys. 100, 62 (1976)]. We believe our approach to be a fundamental generalization of the usual notions about gauge transformations in quantum mechanics.

Original languageEnglish (US)
Pages (from-to)3764-3771
Number of pages8
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume54
Issue number5
DOIs
StatePublished - 1996

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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