A Nonlinear Schrödinger Wave Equation With Linear Quantum Behavior

We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum th...

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Bibliographic Details
Published in:arXiv.org 2014-03
Main Authors: Richardson, Chris D, Schlagheck, Peter, Martin, John, Vandewalle, Nicolas, Bastin, Thierry
Format: Article
Language:English
Subjects:
Nonlinearity
Plancks constant
Quantum mechanics
Quantum physics
Quantum theory
Scaling
Wave equations
Online Access:Get full text
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Summary:We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum theory. The classical wave equation includes a nonlinear classicality enforcing potential which when eliminated transforms the wave equation into the linear Schr\"odinger equation. We show that it is not necessary to completely cancel this nonlinearity to recover the linear behavior of quantum mechanics. Scaling the classicality enforcing potential is sufficient to have quantum-like features appear and is equivalent to scaling Planck's constant.
ISSN:2331-8422
DOI:10.48550/arxiv.1403.2177