Linear and nonlinear analogues of the schrödinger equation in the contextual approach to quantum mechanics

Andrei Yu. Khrennikov

Ervin Kaminski Lenzi, Antonio S. M. de Castro, R. S. Mendes

Chris Richardson, Peter Schlagheck, John Martin +2 more

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.

Pang Xiao‐feng

A nonlinear Schrodinger equation is used to replace the linear Schrodinger equation in quantum mechanics and to study further the stability of microscopic particles by using the minimum theorem of energy and variational theorem. The investigation shows that the microscopic particles described by the nonlinear Shrodinger equation are localized and have a wave–corpuscle duality, which are completely different from that depicted by the linear Schrodinger equation in quantum mechanics. The results obtained by the minimum theorem of energy and variational theorem indicate that the solutions of the nonlinear Schrodinger equation or the microscopic particles are stable. Therefore, the microscopic particles have the feature of classical particles in such a case.

акустика Механика

W. P. Schleich, Daniel M. Greenberger, Donald H. Kobe +1 more