Dirac potential in the Doebner–Goldin equation

A. N. Ikot, Sunday Edet Etuk, HASSAN HASSANABADI +2 more

W. Lücke

Gisin's argument against deterministic nonlinear Schroedinger equations is shown to be valid for every (formally) nonlinearizable case of the general Doebner-Goldin 2-particle equation in the following form: The time-dependence of the position probability distribution of a particle `behind the moon' may be instantaneously changed by an arbitrarily small instantaneous change of the potential `inside the laboratory'.

P. Nattermann, Wolfgang Scherer

Invariants of nonlinear gauge transformations of a family of nonlinear Schrödinger equations proposed by Doebner and Goldin are used to characterize the behaviour of exact solutions of these equations.

Yi-Rong Ma, Wei Jia, Shirong Lin +1 more

This study proposes the usage of an effective potential to investigate a dissipative quantum system with rotational velocity. After gauge transformation, a Doebner- Goldin equation (DGE) that describes the dissipative quantum system with a Dirac potential is obtained. The DGE is solved based on constraint of vertical relation between the rotational velocity field and density gradient when a harmonic oscillator model is considered. It is observed that the dissipative quantum system is directly equivalent to a monopole system and that the two gauge potentials that are given by Wu and Yang in the north and south hemispheres can be reproduced. Furthermore, a set of gauge-invariant parameters is obtained to discuss the dissipation characteristics of the system.