The Dynamic and Collision Features of Microscopic Particles Described by the Nonlinear Schrödinger Equation in the Nonlinear Quantum Systems

Abstract

The dynamic and collision features of microscopic particles described by nonlinear Schrodinger equation are investigated deeply using the analytic and the Runge-Kutta method of numerical simulation. The results show that the microscopic particles have a wave-corpuscle duality and are stable in propagation. When the two microscopic particles are collided, they can go through each other and retain their form after their collision of head-on from opposite directions, This feature is the same with that of the classical particles. However, a wave peak of large amplitude, which is a result of complicated superposition of two solitary waves, occurs in the colliding process. This displays the wave feature of microscopic particles. Therefore, the collision process shows clearly that the solutions of the nonlinear Schrodinger equation have a both corpuscle and wave feature, then the microscopic particles represented by the solutions have a wave-corpuscle duality. Obviously, this is due to the nonlinear interaction b||2. Thus we can determine the nonlinear Schrodinger equation can describe correctly the natures and properties of microscopic particles in quantum systems. Key words: Microscopic particle Schrodinger equation; Wave-corpuscle duality; Nonlinear interaction; Collision; Propagation; Quantum mechanics