A Nonlinear Schr\"odinger Wave Equation With Linear Quantum Behavior
Quantum Physics
2014-03-20 v2
Abstract
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.
Cite
@article{arxiv.1403.2177,
title = {A Nonlinear Schr\"odinger Wave Equation With Linear Quantum Behavior},
author = {Chris D. Richardson and Peter Schlagheck and John Martin and Nicolas Vandewalle and Thierry Bastin},
journal= {arXiv preprint arXiv:1403.2177},
year = {2014}
}