Nonlinear Schrodinger wave equation with linear quantum behavior

作者：Richardson Chris D^*; Schlagheck Peter; Martin John; Vandewalle Nicolas; Bastin Thierry

来源：Physical Review A, 2014, 89(3): 032118.

DOI：10.1103/PhysRevA.89.032118

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%26apos;s constant.

• 出版日期2014-3-13