Symmetry, Local Linearization, and Gauge Classification of the Doebner-Goldin Equation
arXiv:quant-ph/9506037 · doi:10.1016/0034-4877(96)83634-2
Abstract
For the family of nonlinear Schrödinger equations derived by H.-D.~Doebner and G.A.~Goldin (J.Phys.A 27, 1771) we calculate the complete set of Lie symmetries. For various subfamilies we find different finite and infinite dimensional Lie symmetry algebras. Two of the latter lead to a local transformation linearizing the particular subfamily. One type of these transformations leaves the whole family of equations invariant, giving rise to a gauge classification of the family. The Lie symmetry algebras and their corresponding subalgebras are finally characterized by gauge invariant parameters.
17 pages, LaTeX, 1 figure, to appear in Reports on Mathematical Physics
Cited by in corpus (6)
- Nonlocal looking equations can make nonlinear quantum dynamics local
- On Integrable Doebner-Goldin Equations
- Conditional symmetry and spectrum of the one-dimensional Schrödinger equation
- Density matrix interpretation of solutions of Lie-Nambu equations
- Structure of nonlinear gauge transformations
- Resonance broadening theory of Farley-Buneman turbulence in the auroral E-region