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A PROPRIETY LIMIT FOR THE MEAN WAVE IN FUNCTION THEORY OF PARTICLE SYSTEMS

Jean-Louis Destouches

Published Mar 1, 1960• 0 citations
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Abstract

It is shown that under four conditions the mean wave for a great number of particles in the nonlinear functional theory of particles obeys a linear equation with a probability very near unity. This equation is the same as the wave equation in the usual wave mechanics for the corresponding problem. Thus, the linear part of the equation for the uwave in the fanctional theory of particles is determined. (auth)

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NON-RELATIVISTIC FUNCTIONAL THEORY FOR PARTICLE SYSTEMS

Florence A. Aeschlimann

A study was made of the general conditions required to set up a non- relativistic functional theory for systems of particles. Representation of each particle of a system by a space-time function uj(P,T). Formal classification for the particles of the system with respect to indiscernability and the exclusion principle for the fermions. Using the general theory of predictions, the arguments of the functional for predictions are fixed, functional configuration- space is introduced, and the general form of the equation for the predictional elements is determined. Conditions incurred by the limiting cases of the usual wave mechanics for systems and of the single particle in the functional theory of particles. Fundamental principle for the equations of motion concerning the particles of a system: each function uj(P,T) describing a particle of the system obeys a non-linear equation which depends upon the functions u/sub k/(P,T) of the other particles of the system. Brief investigation of the limiting case of classical mechanics. (auth)

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MEAN WAVE OF A PARTICLE SYSTEM IN FUNCTIONAL THEORY

Florence A. Aeschlimann

Some principles of the functional theory of particles and the properties of the center of masses are discussed. The definitions of mean waves and sum wave are given. in particular the mass mean wave (which corresponds to the center of masses) and the uniform mean wave. The global properties of a system can be expressed with these waves (auth)

•Dec 1, 1959•0 citations

PROPERTIES OF FUSED SYSTEMS IN FUNCTIONAL THEORY

Jean-Louis Destouches

S>Several transformations of the fundamental equations for a fused part of a physical system are given in the functional theory of particles. Objectivity of the values of the mj coefficients of the particles in the fusion process is shown. Properties of the diatinguishable waves in a fused pant of a system are derived, and linear phase waves are obtained. The necessary and sufficient conditions for the fusion of two particles are determined, and the properties of the mean wave for a set of fused systems are obtained. The linear equations placed by de Broglie at the base of the fusion theory are deduced. Properties of the mean wave were determined by measurement, and the linear de Broglie equations were obtained (tr-auth)

•Feb 1, 1961•0 citations

THE BARYCENTER IN THE FUNCTIONAL THEORY OF PARTICLE SYSTEMS

Florence A. Aeschlimann

A definition is given of the barycentric wave for a system of n particles in the functional theory, in the relativistic case, and in the non- relativistic case with spin and isospin or without spin. The equation for the barycentric wave in the relativistic case and in the non-relativistic case is derived. The case of particles of the same mass is considered. Motion around the barycenter is discussed, and equations for the relative motion are obtained. The particular case of a two-particle system is considered. (auth)

•Feb 1, 1960•0 citations

The Properties of Microscopic Particles Described by Nonlinear Schrödinger Equation in Nonlinear Quantum Systems

小峰 庞

原有量子力学的由Schrodinger方程不能很好地描述微观粒子的局域特性和波-粒二象性,因此,量子力学必须改进和发展。在非线性系统中我们考虑了粒子之间或它与背景场之间的非线性相互作用,于是必须用非线性Schrodinger方程去描述的微观粒子的状态。至此,微观粒子的状态和特征相对于线性系统发生了根本性的变化。在这种情况下不论外势场如何变化,但非线性Schrodinger方程都能给出具有波-粒二象特性的解,它由包络孤子和一个载波组成,有一个具有确定的位置的质心;同时,微观粒子此时也具有一个确定的质量,能量和动量,和它们遵守的质量,能量和动量守恒定律,在外场作用时粒子是稳定的,并满足经典运动方程和遵守哈密顿方程和拉格朗日方程。于是用非线性Schrodinger方程去描述的微观粒子具有一个明显的的局域特性和波-粒二象性, 从而彻底消除了原有量子力学存在近一个世纪的困难和问题。基于这些新的结果我们可建立起完整和系统的非线性量子力学理论体系,推动量子力学的发展。因此这一研究具有重要意义。 In original quantum mechanics the Schrodinger equation is, in essence, a wave equation, wherein the microscopic particles depicted have only a wave feature, and not a corpuscle nature. These descriptors do not agree only with the Broglie relation of wave-corpuscle duality, but also with experimental results and the traditional knowledge of particle concept. Meanwhile, the theory gives only some approximate solutions. Thus a series of contradictory representations and problems occur in quantum mechanics, which have re-sulted in durative disputations focused on the area of physics and have not led to any united conclusions until now. The only way to solve these problems and difficulties is to develop the quantum mechanics. We inves-tigate in detail wave-corpuscle duality of microscopic particles described by a nonlinear Schrodinger equa-tion in nonlinear quantum systems. Concretely speaking, we here study the properties of the solution of the nonlinear Schrodinger equation, the stability of microscopic particles, invariance 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, and so on. Studied results show that the solution of the nonlinear Schrodinger equation depicting microscopic particles is a soliton and have a wave-corpuscle duality, microscopic particles have always a mass center and possess determinant positions, sizes, mass, mo-mentum, energy and form, their mass, momentum and energy satisfy corresponding conservation laws, their dynamic states can be described by both nonlinear Schrodinger equation and classical Lagrangian and Ham-ilton equations, their motions obey the classical Newton-type law of motion. These properties indicate that the microscopic particles described by a nonlinear Schrodinger equation have a corpuscle nature. However, the solutions of dynamic equation are some solitary waves which are accompanied by a carrier wave to propagate in space-time, and possess certain frequency and wave speed. Thus microscopic particles described by nonlinear quantum mechanics have also wave feature. Thus we can affirm that the microscopic particles depicted by a nonlinear Schrodinger equation have a perfect wave-corpuscle duality, which are in essence different from those in linear quantum mechanics. Based on these results we can establish a new nonlinear quantum mechanics, which can solve these difficulties and problems disputed for about a century in linear quantum mechanics.

Modern Physics•Jan 1, 2011•0 citations

THE THEORY OF PARTICLE SYSTEMS IN THE CAUSAL INTERPRETATION OF WAVE MECHANICS

Joār Andrade e Silva

An attempt is made to show that it is possible to constnuct a theory of particle systems in accord with the basic ideas of the causal interpretation of wave mechanics by the theory of the double solution. After a discussion of the theory of the individual particle, the de Broglie and Vigier theories on the causal interpretation of the theory of systems are examined. It is then shown that it is possible to reframe the analytical mechanics of systems and, in particular, the Hamilton-Jacobi theory in a space with three dimensions. The question of the form of the basic equations in physical space is discussed in detail. The statistical theory of systems of particles of different nature is explained. (J.S.R.)

•Jan 1, 1960•0 citations
It is shown that under four conditions the mean wave for a great number of particles in the nonlinear functional theory of particles obeys a linear equation with a probability very near unity. This equation is the same as the wave equation in the usual wave mechanics for the corresponding problem. Thus, the linear part of the equation for the uwave in the fanctional theory of particles is determined. (auth)
A study was made of the general conditions required to set up a non- relativistic functional theory for systems of particles. Representation of each particle of a system by a space-time function uj(P,T). Formal classification for the particles of the system with respect to indiscernability and the exclusion principle for the fermions. Using the general theory of predictions, the arguments of the functional for predictions are fixed, functional configuration- space is introduced, and the general form of the equation for the predictional elements is determined. Conditions incurred by the limiting cases of the usual wave mechanics for systems and of the single particle in the functional theory of particles. Fundamental principle for the equations of motion concerning the particles of a system: each function uj(P,T) describing a particle of the system obeys a non-linear equation which depends upon the functions u/sub k/(P,T) of the other particles of the system. Brief investigation of the limiting case of classical mechanics. (auth)
S>Several transformations of the fundamental equations for a fused part of a physical system are given in the functional theory of particles. Objectivity of the values of the mj coefficients of the particles in the fusion process is shown. Properties of the diatinguishable waves in a fused pant of a system are derived, and linear phase waves are obtained. The necessary and sufficient conditions for the fusion of two particles are determined, and the properties of the mean wave for a set of fused systems are obtained. The linear equations placed by de Broglie at the base of the fusion theory are deduced. Properties of the mean wave were determined by measurement, and the linear de Broglie equations were obtained (tr-auth)
A definition is given of the barycentric wave for a system of n particles in the functional theory, in the relativistic case, and in the non- relativistic case with spin and isospin or without spin. The equation for the barycentric wave in the relativistic case and in the non-relativistic case is derived. The case of particles of the same mass is considered. Motion around the barycenter is discussed, and equations for the relative motion are obtained. The particular case of a two-particle system is considered. (auth)
原有量子力学的由Schrodinger方程不能很好地描述微观粒子的局域特性和波-粒二象性,因此,量子力学必须改进和发展。在非线性系统中我们考虑了粒子之间或它与背景场之间的非线性相互作用,于是必须用非线性Schrodinger方程去描述的微观粒子的状态。至此,微观粒子的状态和特征相对于线性系统发生了根本性的变化。在这种情况下不论外势场如何变化,但非线性Schrodinger方程都能给出具有波-粒二象特性的解,它由包络孤子和一个载波组成,有一个具有确定的位置的质心;同时,微观粒子此时也具有一个确定的质量,能量和动量,和它们遵守的质量,能量和动量守恒定律,在外场作用时粒子是稳定的,并满足经典运动方程和遵守哈密顿方程和拉格朗日方程。于是用非线性Schrodinger方程去描述的微观粒子具有一个明显的的局域特性和波-粒二象性, 从而彻底消除了原有量子力学存在近一个世纪的困难和问题。基于这些新的结果我们可建立起完整和系统的非线性量子力学理论体系,推动量子力学的发展。因此这一研究具有重要意义。 In original quantum mechanics the Schrodinger equation is, in essence, a wave equation, wherein the microscopic particles depicted have only a wave feature, and not a corpuscle nature. These descriptors do not agree only with the Broglie relation of wave-corpuscle duality, but also with experimental results and the traditional knowledge of particle concept. Meanwhile, the theory gives only some approximate solutions. Thus a series of contradictory representations and problems occur in quantum mechanics, which have re-sulted in durative disputations focused on the area of physics and have not led to any united conclusions until now. The only way to solve these problems and difficulties is to develop the quantum mechanics. We inves-tigate in detail wave-corpuscle duality of microscopic particles described by a nonlinear Schrodinger equa-tion in nonlinear quantum systems. Concretely speaking, we here study the properties of the solution of the nonlinear Schrodinger equation, the stability of microscopic particles, invariance 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, and so on. Studied results show that the solution of the nonlinear Schrodinger equation depicting microscopic particles is a soliton and have a wave-corpuscle duality, microscopic particles have always a mass center and possess determinant positions, sizes, mass, mo-mentum, energy and form, their mass, momentum and energy satisfy corresponding conservation laws, their dynamic states can be described by both nonlinear Schrodinger equation and classical Lagrangian and Ham-ilton equations, their motions obey the classical Newton-type law of motion. These properties indicate that the microscopic particles described by a nonlinear Schrodinger equation have a corpuscle nature. However, the solutions of dynamic equation are some solitary waves which are accompanied by a carrier wave to propagate in space-time, and possess certain frequency and wave speed. Thus microscopic particles described by nonlinear quantum mechanics have also wave feature. Thus we can affirm that the microscopic particles depicted by a nonlinear Schrodinger equation have a perfect wave-corpuscle duality, which are in essence different from those in linear quantum mechanics. Based on these results we can establish a new nonlinear quantum mechanics, which can solve these difficulties and problems disputed for about a century in linear quantum mechanics.
An attempt is made to show that it is possible to constnuct a theory of particle systems in accord with the basic ideas of the causal interpretation of wave mechanics by the theory of the double solution. After a discussion of the theory of the individual particle, the de Broglie and Vigier theories on the causal interpretation of the theory of systems are examined. It is then shown that it is possible to reframe the analytical mechanics of systems and, in particular, the Hamilton-Jacobi theory in a space with three dimensions. The question of the form of the basic equations in physical space is discussed in detail. The statistical theory of systems of particles of different nature is explained. (J.S.R.)