The wave-corpuscle properties of microscopic particlesin the nonlinear quantum-mechanical systems

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.

The Natures of Microscopic Particles Depicted by Nonlinear Schrodinger Equation in Quantum Systems

When the microscopic particles was depicted by linear Schrodinger equation, we find that the particles have only a wave feature, thus, a series of difficulties and intense disputations occur in quantum mechanics. These problems excite us to consider the nonlinear interactions among the particles or between the particle and background field, which is completely ignored in quantum mechanics. Thus we use the nonlinear Schrodinger equation to describe the natures of microscopic particles. In this case the natures and features of microscopic particles are considerably different from those in quantum mechanics, where the microscopic particles are localized and have truly a wave-particle duality. Meanwhile, they satisfy both the classical dynamics equation and Lagrangian and Hamilton equations and obey the conservation laws of mass, energy and momentum. These natures and features are due to the nonlinear interactions, which are generated in virtue of the interaction between the moved particles and background field through the mechanisms of self-trapping, self-focus and self-condensation. Finally, we verified experimentally the localization and wave-corpuscle features of microscopic particles described by the nonlinear Schrodinger equation using the properties of water soliton and optical-soliton depicted also by the nonlinear Schrodinger equation in water and optical fiber, respectively. Therefore, the new nonlinear quantum theory established on the basis of nonlinear Schrodinger equation is correct and credible. From this investigation we can not only solve difficulties and problems disputed for about a century by plenty of scientists in quantum mechanics but also promote the development of physics and enhance the knowledge and recognition levels to the essences of microscopic matter.

在非线性系统中的微观粒子的特性和非线性量子力学理论(上)

在非线性系统中由于存在着与粒子状态相关的非线性相互作用 ,微观粒子的状态和特征相对于线性系统而发生了很大变化。原有的线性型的量子力学理论不能很好地描述这些微观粒子的状态和特征。至此 ,必然要发展新的理论。本文研究了微观粒子在非线性作用下的运动特性和本性的变化 ,说明了在线性作用和非线性场中微观粒子的性质是明显不同的 ,启示我们必须建立微观粒子在非线性场中运动的新理论。接着我们研究了与微观量子效应迥然不同的宏观量子效应与非线性作用的孤立子运动的紧密关系 ,结合现代孤立子理论和超导与超流理论 ,我们首先提出了非线性量子力学的基本原理及在此基础上建立了系统、完整的非线性量子力学理论体系 ,并得到的一些新结论。最后我们还论证了这个理论的正确性和自洽性 ,它的运用范围以及它的重大意义。

非线性量子力学的建立

笔者在长期研究工作的基础上,从提出非线性量子力学的基本原理出发,建立起了非线性量子力学理论,形成了完整的非线性量子力学的理论体系。从而把量子力学从线性领域推广和发展到非线性领域。在本文中笔者描述了建立这个非线性量子力学的物理背景,它的基本构思,研究的技术路线,产生的实际效果,与国际同类研究比较,本研究的创新和特点以及研究的重大意义。

在非线性系统中的微观粒子的特性和非线性量子力学理论(下)

在非线性系统中由于存在着与粒子状态相关的非线性相互作用 ,微观粒子的状态和特征相对于线性系统而发生了很大变化。原有的线性型的量子力学理论不能很好地描述这些微观粒子的状态和特征。至此 ,必然要发展新的理论。本文研究了微观粒子在非线性作用下的运动特性和本性的变化 ,说明了在线性作用和非线性场中微观粒子的性质是明显不同的 ,启示我们必须建立微观粒子在非线性场中运动的新理论。接着我们研究了与微观量子效应迥然不同的宏观量子效应与非线性作用的孤立子运动的紧密关系 ,结合现代孤立子理论和超导与超流理论 ,我们首先提出了非线性量子力学的基本原理及在此基础上建立了系统、完整的非线性量子力学理论体系 ,并得到的一些新结论。最后我们还论证了这个理论的正确性和自洽性 。