Xiao-feng Pang

Abstract: We debate first the properties of quantum mechanics and its difficulties and the reasons resulting in these diffuculties and its direction of development. The fundamental principles of nonlinear quantum mechanics are proposed and established based on these shortcomings of quantum mechanics and real motions and interactions of microscopic particles and backgound field in physical systems. Subsequently, the motion laws and wave-corpuscle duality of microscopic particles described by nonlinear Schr?dinger equation are studied completely in detail using these elementary principles and theories. Concretely speaking, we investigate the wave-particle duality of the solution of the nonlinear Schr?dinger equation, the mechanism and rules of particle collision and the uncertainty relation of particle’s momentum and position, and so on. We obtained that the microscopic particles obey the classical rules of collision of motion and satisfy the minimum uncertainty relation of position and momentum, etc. From these studies we see clearly that the moved rules and features of microscopic particle in nonlinear quantum mechanics is different from those in linear quantum mechanics. Therefore, nolinear quantum mechanics is a necessary result of development of quantum mechanics and represents correctly the properties of microscopic particles in nonlinear systems, which can solve difficulties and problems disputed for about a century by scientists in linear quantum mechanics field.

Keywords: Microscopic Particle; NonlinearInteraction; Quantum Mechanics; Nonlinear Schrödinger Equation; Basic Principle; Nonlinear Theory; Wave-Particle Duality; Motion Rule

Cite this paper: Pang, X. (2011) The wave-corpuscle properties of microscopic particlesin the nonlinear quantum-mechanical systems. Natural Science, 3, 600-616. doi: 10.4236/ns.2011.37083.

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