1997/03/12 by P. Nattermann, Nattermann, Peter
Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #High Energy Physics - Theory (hep-th) #Mechanical and Optical Resonators #Nonlinear Photonic Systems #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.quant-ph/9703017
openalex publication_date 1997/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the problems of interpretation of a nonlinear evolution equation in quantum mechanics we discuss in this contribution the concept of nonlinear gauge transformations, that has recently been introduced in joint work with Doebner and Goldin, in the framework of Mielnik's Generalized Quantum Mechanics. Using these gauge transformations we construct linear quantum systems in a ``nonlinear disguise'', and a gauge generalization of these (in analogy to the minimal coupling of orthodox quantum mechanics) leads to a unification of Bialynicki-Birula--Mycielski and Doebner--Goldin evolution equations for the quantum system. The notion of nonlinear observables introduced by Lücke is finally discussed in the same framework.