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arXiv:quant-ph/9710033

Gisin Nonlocality of the Doebner-Goldin 2-Particle Equation

W. Lücke

Published Oct 13, 1997• 6 citations
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Abstract

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'.

DOI
10.48550/arxiv.quant-ph/9710033

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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'.
We propose a new, nonlinear representation-independent generalized Schrodinger equation, satisfying the homogeneity condition, which is valid for arbitrary representations and arbitrary operators. This is a generalization of the equation recently proposed by Doebner and Goldin(1992) for the wavefunction written in Cartesian coordinates. The new model leads to simple exact solutions describing, for instance, the relaxation of the two-level system and the harmonic oscillator, both in Fock and in coherent states bases.