Influences of externally applied potential on the properties of microscopic particles in nonlinear quantum systems

When the Schrödinger equation in quantum mechanics is replaced by the nonlinear Schrödinger equation to describe microscopic particles in nonlinear quantum systems, it has been verified that the nature of the particles differs considerably from those in quantum mechanics, where they are localized and have also wave-corpuscle duality due to the nonlinear interactions. In this case the influences of externally applied potentials in the nonlinear Schrödinger equation on the natures of the microscopic particles have been studied by a perturbation theory. The studied results show that the external potential can change the states of the microscopic particles, such as the positions, amplitude and wave forms, but cannot change the wave-corpuscle duality. In the meanwhile, we find further that the relationship between the external potential and change of positions of the particle satisfies the rule of motion of classical particles. Thus we know from this study that the kinetic energy term, (ℏ2/2m)∇2ϕ, in the nonlinear Schrödinger equation can only make the microscopic particles have a wave feature, but the nonlinear interaction b|ϕ|2ϕ determines its corpuscle feature, their combination makes the microscopic particles have a wave-corpuscle duality, and the potential V(r⇒,t)ϕ changes only the positions, amplitude and wave form of the particles. Therefore the nonlinear interaction plays an important role in determination of the wave-corpuscle duality of microscopic particles in quantum theory.