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Establishment of New Theory of Nonlinear Quantum Mechanics and its Correctness

Research Area: Volume 1 Issue 1, April - 2013 Year: 2013
Type of Publication: Article Keywords: microscopic particle, nonlinear interaction, quantum mechanics, nonlinear systems, nonlinear Schrödinger equation, basic principle, nonlinear theory, wave-particle duality
Authors:
  • Pang Xiao-feng
Journal: IJNIST Volume: 1
Number: 1(4) Pages: 25-78
Month: March
Abstract:
We here establish a new theory of nonlinear quantum mechanics and discuss further its correct in detian. In this case we debate first the properties of quantum mechanics and its difficulties and problems, the reasons resulting in these diffuculties and direction of development of quantum mechanics are investigated in detail. For solving these difficulties of quantum mechanics, describing real laws of motion of microscopic particles in physical systems and studying correctly properties of complicated systems the elementary principles and theory of nonlinear quantum mechanics are proposed and established based on these problems in quantum mechanics, properties of macroscopic quantum effect and theories of superconductivity and superfluidity. Subsequently, the motion laws and some main properties of microscopic particles in nonlinear quantum systems are studied completely using these elementary principles and theories. Concretely speaking, we investigate in this paper the wave-particle duality of the solution of the nonlinear Schrödinger equation, the stability of microscopic particles described by nonlinear quantum mechanics, invariances and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations, the classical rule of microscopic particle motion, the mechanism and rules of particle collision, the features of reflection and the transmission of particles at interfaces, and the uncertainty relation of particle’s momentum and position, and so on. We obtained a lot of new and interesting results from this investigation, for example, the microscopic particles have obviously 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, obey the general invariance and conservation laws of mass, energy and momentum and angular momentum, their motions satisfy not only the nonlinear Schrödinger equation but also classical equation of motion, Hamilton equation, Lagrangian equation and classical rule of collision of paperties. Therefore the particles have a corpuscle feature. Meanwhile, these microscopic particles have certain frequency and amplitude, can generate reflection and transmission at the interfaces, thus they havealso a wave feature, which but are different from linear and KdV solitary wave’s. These natures and rules of motion of microscopic particle in nonlinear quantum mechanics is completely different from those in quantum mechanics. Hence we conclude that nolinear quantum mechanics is a new and correct physics theory 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. Therefore the nonlinear quantum mechanics established by us can promote the development of physics and enhance and raise the knowledge and recognition levels to the essences of microscopic matter. We can predict that it has extensive applications in physics, chemistry, biology and polymers, etc.
Full text: IJNIST4.pdf

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