Nonlinear quantum mechanics: A necessary result of development of quantum mechanics

A.B. Datzeff

Pang Xiao‐feng

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.

Pang Xiao‐feng

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.

Gilbert Reinisch

Pang Xiao Feng

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.

Pang Xiao Feng