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MEAN WAVE OF A PARTICLE SYSTEM IN FUNCTIONAL THEORY

Florence A. Aeschlimann

Published Dec 1, 1959• 0 citations
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Abstract

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)

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Acta Physica Sinica•Jan 1, 1993•1 citation
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)
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 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)
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)
The center-of-mass principle is the key to the rapid computation of the interaction of a large number of classical particles. Electrons governed by the multiparticle Schrödinger equation have a much more complicated interaction mainly due to their spatial extent and the antisymmetry constraint on the total wave function of the combined electron system. We present a center-of-mass principle for quantum particles that accounts for this spatial extent, the antisymmetry constraint, and the potential operators. We use it to construct an algorithm for computing a size-consistent approximate wave function for large systems with simple geometries.
Double wave quantum theory is applied to describe the motion of charged particle in a uniform magnetic field. This description of the motion of the particle is complete. One can tell the value of an arbitrary physical quantity at any time. The probability and the formula to calculate mean values in ordinary quantum mechanics comes from the average of double wave description over a certain ensemble. The rule of gauge transformation in quantum mechanics can be seen from the average over an ensemble.