Nonlinear Schrodinger wave equation with linear quantum behavior

被引：29

作者：

Richardson, Chris D. ^{[1
]}

Schlagheck, Peter ^{[1
]}

Martin, John ^{[1
]}

Vandewalle, Nicolas ^{[1
]}

Bastin, Thierry ^{[1
]}

机构：

[1] Univ Liege, Dept Phys, B-4000 Liege, Belgium

来源：

PHYSICAL REVIEW A | 2014年 / 89卷 / 03期

关键词：

Nonlinear equations - Mathematical transformations - Control nonlinearities - Wave equations;

D O I：

10.1103/PhysRevA.89.032118

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

We show that a nonlinear Schrodinger 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 Schrodinger 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.

引用

页数：4

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