Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Nonlinear Generalisation of Quantum Mechanics

Version 1 : Received: 23 August 2021 / Approved: 27 August 2021 / Online: 27 August 2021 (14:03:12 CEST)
Version 2 : Received: 12 October 2021 / Approved: 14 October 2021 / Online: 14 October 2021 (15:11:22 CEST)

How to cite: Jamali, A. Nonlinear Generalisation of Quantum Mechanics. Preprints 2021, 2021080525 (doi: 10.20944/preprints202108.0525.v2). Jamali, A. Nonlinear Generalisation of Quantum Mechanics. Preprints 2021, 2021080525 (doi: 10.20944/preprints202108.0525.v2).

Abstract

It is known since Madelung that the Schrödinger equation can be thought of as governing the evolution of an incompressible fluid, but the current theory fails to mathematically express this incompressibility in terms of the wavefunction without facing problem. In this paper after showing that the current definition of quantum-mechanical momentum as a linear operator is neither the most general nor a necessary result of the de Broglie hypothesis, a new definition is proposed that can yield both a meaningful mathematical condition for the incompressibility of the Madelung fluid, and nonlinear generalisations of Schrödinger and Klein-Gordon equations. The derived equations satisfy all conditions that are expected from a proper generalisation: simplification to their linear counterparts by a well-defined dynamical condition; Galilean and Lorentz invariance (respectively); and signifying only rays in the Hilbert space.

Keywords

quantum mechanics; foundations of quantum mechanics; nonlinear equation; nonlinear quantum mechanics; nonlinear schrödinger equation

Comments (1)

Comment 1
Received: 14 October 2021
Commenter: Alireza Jamali
Commenter's Conflict of Interests: Author
Comment: Abstract revised and expanded
* The part on Weinberg's Homogeneity condition corrected
* Conclusion section added
* References updated and improved
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