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

Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positiona l measurements at different times, we characterize directly a class of nonl inear quantum theories physically equivalent to linear quantum mechanics th rough nonlinear gauge transformations. We show that under two physically mo tivated assumptions, these transformations are uniquely determined: they ar e exactly the group of time-dependent, nonlinear gauge transformations intr oduced previously for a family of nonlinear Schrodinger equations. The gene ral equation in this family, including terms considered by Kostin, by Bialy nicki-Birula and Mycielski, and by Doebner and Goldin, with time-dependent coefficients, can be obtained from the linear Schrodinger equation through gauge transformation and a subsequent process we call gauge generalization. We thus unify, on fundamental grounds, a rather diverse set of nonlinear t ime evolutions in quantum mechanics. (C) 1999 American Institute of Physics . [S0022-2488(98)04011-0].