Nonlinear Quantum Mechanics and Its Correctness
Authors:   University of Electronic Science and Technology of China, China., PANG XIAOFENG 
Published: January 2024

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.