2014/03/11 by Chris Richardson, Chris D. Richardson, Peter Schlagheck +3 · 1 citation
Computer Science · Physics and Astronomy · #Mechanical and Optical Resonators #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.89.032118
arxiv created 2014/03/11 · openalex publication_date 2014/03/13 · arxiv updated 2014/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 quantumlike features appear and is equivalent to scaling Planck's constant.