[en] We show that a nonlinear Schroedinger 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 Schro ̈dinger 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.
Disciplines :
Physics
Author, co-author :
Richardson, Christopher ; Université de Liège - ULiège > Département de physique > Physique quantique statistique
Schlagheck, Peter ; Université de Liège - ULiège > Département de physique > Physique quantique statistique
Martin, John ; Université de Liège - ULiège > Département de physique > Optique quantique
Vandewalle, Nicolas ; Université de Liège - ULiège > Département de physique > Physique statistique
Bastin, Thierry ; Université de Liège - ULiège > Département de physique > Spectroscopie atomique et Physique des atomes froids
Language :
English
Title :
Nonlinear Schrödinger wave equation with linear quantum behavior
Publication date :
2014
Journal title :
Physical Review. A, Atomic, molecular, and optical physics
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