Berlin 2014 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 11: Quantenmechanik

MP 11.3: Talk

Thursday, March 20, 2014, 17:10–17:30, SPA SR125

A Nonlinear Schrödinger Wave Equation With Linear Quantum Behavior — •Chris D. Richardson, Peter Schlagheck, John Martin, Nicolas Vandewalle, and Thierry Bastin — Département de Physique, University of Liege, 4000 Liege, Belgium

We show that a nonlinear Schrödinger 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 Schrödinger 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.