The dynamic natures of microscopic particles described by nonlinear Schrödinger equation

Abstract

There are a lot of difficulties and troubles in quantum mechanics, when the linear Schrodinger equation is used to describe microscopic particles. Thus, we here replace it by a nonlinear Schrodinger equation to investigate the properties and rule of microscopic particles. In such a case we find that the motion of microscopic particle satisfies classical rule and obeys the Hamiltonian principle, Lagrangian and Hamilton equations. We verify further the correctness of these conclusions by the results of nonlinear Schrodinger equation under actions of different externally applied potential. From these studies, we see clearly that rules and features of motion of microscopic particle described by nonlinear Schrodinger equation are greatly different from those in the linear Schrodinger equation, they have many classical properties, which are consistent with concept of corpuscles. Thus, we should use the nonlinear Schrodinger equation to describe microscopic particles.