%0 Journal Article
%T Gauge Transformations in Quantum Mechanics and the Unification of Nonlinear Schr£żdinger Equations
%A H. -D. Doebner
%A G. A. Goldin
%A P. Nattermann
%J Mathematics
%D 1997
%I arXiv
%R 10.1063/1.532786
%X 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 for a family of nonlinear Schr\"odinger 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 Schr\"odinger 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.
%U http://arxiv.org/abs/quant-ph/9709036v1