A Nonlinear Approach for Quantum Mechanics

Abstract

This work represents a possible way to achieve the Einstein-de Broglie soliton-particle concept. The weakly nonlinear Klein-Gordon equation (nonlinear quantum mechanics) is investigated by the asymptotic perturbation (AP) method for a particle confined in a box. The quantization of the energy with a slight difference with respect to the standard (linear) quantum mechanics is obtained. Both relativistic and non-relativistic cases are considered and the transition frequencies are slightly different for the linear and nonlinear quantum mechanics. Experimental verification is needed to choose between the two theories.