For the development of quantum mechanics from linear range to nonlinear domain the author work at and investigate this problem about 20 years.He firstly sought the roots of these problems existed in the LQM.When restrictions of the elementary hypotheses for the independence of the Hamiltonian of the systems on the states of the particles and the linearity of the theory in the LQM were broken through he proposed and established elementary principles and theory of the NLQM according to the features and theory of macroscopic quantum effects and soliton theory,found out further the properties and rules of motion of the MIPs in the nonlinear systems.He discovers that the laws of motion of the MIPs in such a case are completely different from that in the LQM.They have a lot of new properties.Therefore the NLQM is a new subject,it could solve these problems disputed long-times about one centenary by the scientists in the LQM.Meanwhile,the self-consistence and validity of this theory have been also checked,we can give a lot of new results and explain a large number of physical phenomena,if it is utilized in physics,biology and polymer.Thus the NLQM is a necessary result of development of quantum mechanics and correct representation form in the nonlinear systems.Establishing the NLQM can promotes development of physics and can raise the knowledge and recognition levels to the essences of the microscopic matters.Therefore,the NLQM built has important science meanings.
For the development of quantum mechanics from linear range to nonlinear domain the author work at and investigate this problem about 20 years.He firstly sought the roots of these problems existed in the LQM.When restrictions of the elementary hypotheses for the independence of the Hamiltonian of the systems on the states of the particles and the linearity of the theory in the LQM were broken through he proposed and established elementary principles and theory of the NLQM according to the features and theory of macroscopic quantum effects and soliton theory,found out further the properties and rules of motion of the MIPs in the nonlinear systems.He discovers that the laws of motion of the MIPs in such a case are completely different from that in the LQM.They have a lot of new properties.Therefore the NLQM is a new subject,it could solve these problems disputed long-times about one centenary by the scientists in the LQM.Meanwhile,the self-consistence and validity of this theory have been also checked,we can give a lot of new results and explain a large number of physical phenomena,if it is utilized in physics,biology and polymer.Thus the NLQM is a necessary result of development of quantum mechanics and correct representation form in the nonlinear systems.Establishing the NLQM can promotes development of physics and can raise the knowledge and recognition levels to the essences of the microscopic matters.Therefore,the NLQM built has important science meanings.
The properties of quantum mechanics and its difficulties and problems are discussed, the reasons resulting in these diffuculties and direction of development of quantum mechanics are carefully studied. In practice, quantum mechanics neglects the real motions of the microscopic particles and backgound field as well as the real interactions between them. Therefore it can describe appromately the states of microsco[ic particles. For solving these difficulties of quantum mechanics, we proposed and established a nonlinear quantum mechanics based on the properties of macroscopic quantum effect and theories of superconductivity and superfluidity. In the new theory the elementary principles are proposed, its properties are also investigated. Subsequently, the motion laws and some main properties of microscopic particles in nonlinear quantum systems, includong the wave-particle duality of the solution of the nonlinear Schrodinger equation, the stability of microscopic particles described by nonlinear quantum mechanics and the classical rule of microscopic particle motion, are studied using these elementary principles and theories. We obtained a lot of new and interesting results from this investigation, for example, the microscopic particles have really a wave-corpuscle duality in nonlinear quantum mechabics. The microscopic particles are localized due to the nonlinear interaction, have a determinant size, mass, energy and momentum. Thus the microscopic particles have not only a corpuscle but also a wave features, which are completely different from those in quantum mechanics. Hence we conclude that nolinear quantum mechanics is a new physical theory, a correct representation of describing microscopic particles and a necessary result of the development of quantum mechanics, but traditional quantum mechanics is only its an approximation and especial case at the nonlinear interaction to be equal to zero, it can solve the difficulties and problems disputed for about a century by scientists in quantum mechanics field. In the meanwhile, we use the new theory of nonlinear quantum mechanics to study properties of the excitons and phonons in an organic crystry (acetanilide). The results obtained show that the excitons and phonons become as a soliton having a wave-corpuscle duality in this system.Thus the correctness and avialablity of nonlinear quantum mechanics are demontrated using these experiments. We can predict that it has extensive applications in physics, chemistry, biology and polymers, etc.. Finally we state how the difficulties and problems in quantum mechanics are solved by the new theory of nonlinear quantum mechanics. Thus we can affirm from these investigations that the nonlinear quantum mechanics established by us is correct, quantum mechanics is only an appromate theory.
Linear Quantum Mechanics (LQM): Its Successes and Problems Macroscopic Quantum Effects and Properties of Motion of Quasiparticles The Fundamental Principles and Theories of Nonlinear Quantum Mechanics Wave-Corpuscle Duality of Microscopic Particles (MIP) in the NLQM Nonlinear Interaction and Localization of the MIP Nonlinear Versus Linear Quantum Mechanics The Problems Solving in the NLQM Properties and States of the MIP in Different Nonlinear Systems Nonlinearly Quantum-Mechanical Properties of the Excitons and Phonons Properties of Nonlinear Excitations and Motions for Protons, Polarons and Magnons in Different Systems.
The basic principles of quantum mechanics, which is the foundations of model science, and, its difficulties and contradictions are exhibited and confirmed in detail and systematically by plenty of the experimental facts and theoretical results obtained from the solutions of basic Schrödinger equation through their comparisons of the intrinsic features of wave and corpuscle of the microscopic particles between the theoretical results and experimental facts. A basic difficulty is that the microscopic particles described by this linear theory have only a wave, not wave and corpuscle duality, which is inherent of quantum mechanics and cannot all be changed in the framework of the linear theory no matter what variations of investigated ways and methods, i.e., these difficulties and contradictions determinate and affirm that original quantum mechanics must be remoulded completely and developed forward. Its only direction of development is to establish nonlinear quantum mechanics, its some ideas and principles were proposed and suggested by a great number of researchers and authors over the past few decades, but they are not successful. But new nonlinear quantum mechanics proposed by Pang gave a perfect wave-corpuscle dulauty of microscopc particles and established a complete and systematical principle and theory. Thus, we afformed and confirmed the correctness of the new nonlinear quantum theory. In order to verify further the validity of the new nonlinear theory we elucodate and explain again that the nonlinear interactions existed in the new theory are wide and real existences in all physical systems, they were generated by virtue of five mechanisms for self-interaction, self-trapping, self-forcusing, self-considering and self-localizing. At the same time, we researched and exhibiteed fully the concrete representions of nonlear interaction for commom microscopic particles such as the electron, exciton, proton, plaron, photon, phonon and magneton, which are all consistent from those in Pang’s nonlinear quantum mechanics. These investigations and results proved also that Pang’s nonlinear quantum mechanics is correct and exact. Finally, we verified and confirmed completely the correctness of Pang’s new nonlinear theory using the experimental results of the property of movements of nonlinear solitons occurred in water and light fibers, in which the n, the dynamic equations of the water soliton and photon solito are all described by the nonlinear Schrödiger equation. Hence, their results and experimental evidences of wave-corpuscle duality of microscopic particles veried the correctness of Pang’s nonlinear quantum mechanics. Then we can use Pang’s theory to research the properties of microscopic particles in differet systems. These problems, the rules of motion of the particles as well as 396 reference papers are contained in the e-book for the reders. The concrete content his involved by e-book are described the follows. Chapter 1. The basic principles of quantum mechanism and its dificults and contradictions; Chapter 2. The necessarity remoulding quantum mechanics and establishment of nonlinear quantum mechanics; Chapter 3. The wave-corpuscle duality of microscopic particles in Pang’s nonlinear quantum mechanics; Chapter 4. Real and wide existences of nonlinear interactions as well as their mechanisms of generation in physical systems; Chapter 5. The nonlinear dynamic properities of common microscopic particles in different physical systems; Chapter 6. The experimental evidences for the correctness of nonlinear quantum mechanics. This e-book is intended and learned for researchers, teachers, graduate students and upper level undergraduate students.
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.
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 states properties of the microscopic particles in the nonl inear systems occur great changes relati vely to that in the linear systems due t o the nonlinear interactions related to its states we found from the practical s tudies.Original quantum mechanics is lin ear in which there are a lot of difficul ties,for example,the wave-corpuscle dual ity of the microscopic particle,which ca nnot be solved in the framework of this theory.It cannot be used to describe the laws of motion of the microscopic parti cles in nonlinear systems.Therefore,it i s very necessary to develop continuously the quantum mechanics into the nonlinea r systems.Based on the close relations a mong the nonlinear interaction and solit on motions and macroscopic quantum effec t,incorporating modern theories of super conductor and superfluid and soliton we proposed and established the fundamental principles and theory of nonlinear quan tum mechanics and established its theore tical system.Meanwhile,we give the featu res of this theory and verified its vali dity and self-consistence by modern nonl inear and soliton theories.