Publications (7)
Symmetry, Local Linearization, and Gauge Classification of the Doebner-Goldin Equation
P. Nattermann
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 subfami…
A FAMILY OF NONLINEAR SCHRÃDINGER EQUATIONS: LINEARIZING TRANSFORMATIONS AND RESULTING STRUCTURE
H. -D. Doebner, G. A. Goldin, P. Nattermann
We examine a recently-proposed family of nonlinear Schrödinger equations [J. Phys. A: Math. Gen. 27:1771(1994)] with respect to a group of transformations that linearize a subfami…
On Integrable Doebner-Goldin Equations
P. Nattermann, R. Zhdanov
We suggest a method for integrating sub-families of a family of nonlinear {\sc Schrödinger} equations proposed by {\sc H.-D.~Doebner} and {\sc G.A.~Goldin} in the 1+1 dimensional…
Borel Quantization: Kinematics and Dynamics
H. -D. Doebner, P. Nattermann
In this contribution we review results on the kinematics of a quantum system localized on a connected configuration manifold and compatible dynamics for the quantum system includin…
Nonlinear Quantum Mechanics and Locality
W. Luecke, P. Nattermann
It is shown that, in order to avoid unacceptable nonlocal effects, the free parameters of the general Doebner-Goldin equation have to be chosen such that this nonlinear Schrödinge…
Gauge Transformations in Quantum Mechanics and the Unification of Nonlinear Schrödinger Equations
H. -D. Doebner, G. A. Goldin, P. Nattermann
Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different ti…