Research
The Difficulties of Quantum Mechanics and its Investigations of Development
When the states and properties of microscopic particles were described by linear SchrÖdinger equation the quantum mechanics had a lot of difficulties, which cause a centenary controversy in physics and have not a determinate conclusions till now. Thus we used a nonlinear SchrÖdinger equation to replace the linear SchrÖdinger equation and to depict and study in detail the states, properties and rules of motion of microscopic particles. Concretely speaking, we here investigated the properties and rules of wave-particle duality of microscopic particles and its stability, the invariances and conservation laws of motion of particles, the classical rule of motion, Hamiltonian principle of particle motion, corresponding Lagrangian and Hamilton equations for the microscopic particle, the mechanism and rules of particle collision in different nonlinear systems, the uncertainty relation of position and momentum of particles, the features of reflection and transmission of the particles at interfaces as well as the eigenvalue and eigenequations of the particles, and so on. The results obtained from these investigations show clearly that the microscopic particles described by the nonlinear SchrÖdinger equation have exactly a wave- particle duality, motions of its centre of mass meet not only classical equation of motion but also the Lagrangian and Hamilton equations, its mass, energy and momentum and angular momentum satisfy corresponding invariances and conservation laws, their collision has the feature of collision of classical particles, the uncertainty of position and momentum of the particles has a minimum, it is a bell-type solitary wave contained envelope and carrier wave, which but differs from not only KdV solitary wave but linear wave, its eigenvalues and eigenequations obey Lax principle and possess plenty of unusual peculiarities. The above natures and properties of the particles are different completely and in essence from those described the linear SchrÖdinger
The Mechanism of Generation of Nonlinear Interactions of Microscopic Particles and its Properties in Quantum Systems
The mechanisms of generation of the nonlinear interactions in the quantum systems are studied using a nonlinear Schrodinger equation, which can describe the states and properties of motion of the microscopic particles. The investigations show that the interactions arises from the interaction between the moved particle and background field. the difficulties, limitations and approximations of the quantum mechanics and its roots and reasons are first revealed and pointed out. The quantum mechanics simplifies and blots out the real motions and interactions of the microscopic particles including the nonlinear interactions, thus the particles have only a wave feature, not corpuscle feature. In view of these problems and difficulties we add the nonlinear interaction, φ φ 2 b , into the dynamic equation and use again it to describe the particles. Thus the wave or dispersive effect of the particles is suppressed by the nonlinear interactions, thus its localization and wave-corpuscle duality are displayed and exhibited naturally. Subsequently, we investigate the features of the particles and find that the nonlinear interactions exist always, if and only if the real motions of the particles and background fields as well as the interactions between them are considered simultaneously. On the basis of analyses of dynamics of the electrons and nucleon or lattice (background) fields we give two mechanisms of self-interaction and selftrapping for the generation of nonlinear interactions and corresponding representations. Finally we discuss the properties of the nonlinear interactions in the two mechanisms and obtain the relations between the action and counteraction of the two nonlinear interactions of the particles and background fields. We find that although the nonlinear interaction accepted by the particles and background field can generate simultaneously in the nonlinear quantum systems, the two nonlinear interactions do not completely satisfy the law of action and counteract
