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Einstein-De Broglie relations on the lattice  [PDF]
M. Lorente
Physics , 2004,
Abstract: Historically the starting point of wave mechanics is the Planck and Einstein-de Broglie relations for the energy and momentum of a particle, where the momentum is connected to the group velocity of the wave packet. We translate the arguments given by de Broglie to the case of a wave defined on the grid points of a space-time lattice and explore the physical consequences such as integral period, wave length, discrete energy, momentum and rest mass.
Applications of the Characteristic Theory to the Madelung-de Broglie-Bohm System of Partial Differential Equations: The Guiding Equation as the Characteristic Velocity  [PDF]
Javier Gonzalez,Xavier Gimenez,Josep Maria Bofill
Physics , 2007,
Abstract: First, we use the theory of characteristics of first order partial differential equations to derive the guiding equation directly from the Quantum Evolution Equation (QEE). After obtaining the general result, we apply it to a set of evolution equations (Schroedinger, Pauli, Klein-Gordon, Dirac) to show how the guiding equation is, actually, the characteristic velocity of the corresponding matter field equations.
Relating the probability distribution of a de Broglie wave to its phase velocity
PingXiao Wang,JiaXiang Wang,YuKun Huo,Werner Scheid,Heinrich Hora
Chinese Science Bulletin , 2012, DOI: 10.1007/s11434-012-5051-0
Abstract: We show that the phase velocity in a stationary state of a de Broglie wave can be directly obtained from the probability distribution, i.e. the quantum trajectories, without detailed knowledge of the phase term itself. In other words, the amplitude of a de Broglie wave function describes not only the probability distribution but also the phase velocity distribution. Using this relationship, we comment on two calculations of the Goos-H nchen shift in de Broglie waves.
Developing de Broglie Wave
Zheng-Johansson J. X.,Johansson P.-I.
Progress in Physics , 2006,
Abstract: The electromagnetic component waves, comprising together with their generating oscillatory massless charge a material particle, will be Doppler shifted when the charge hence particle is in motion, with a velocity v, as a mere mechanical consequence of the source motion. We illustrate here that two such component waves generated in opposite directions and propagating at speed c between walls in a one-dimensional box, superpose into a traveling beat wave which resembles directly L. de Broglie’s hypothetic phase wave. This phase wave in terms of transmitting the particle mass at the speed v and angular frequency Omega obeying the de Broglie relations, represents a de Broglie wave. The standing-wave function of the de Broglie (phase) wave and its variables for particle dynamics in small geometries are equivalent to the eigen-state solutions to Schroedinger equation of an identical system.
A Geometric Approach to the Quantum Mechanics of de Broglie and Vigier  [PDF]
W. R. Wood,G. Papini
Physics , 1996,
Abstract: Following de Broglie and Vigier, a fully relativistic causal interpretation of quantum mechanics is given within the context of a geometric theory of gravitation and electromagnetism. While the geometric model shares the essential principles of the causal interpretation initiated by de Broglie and advanced by Vigier, the particle and wave components of the theory are derived from the Einstein equations rather than a nonlinear wave equation. This geometric approach leads to several new features, including a solution to the de Broglie variable mass problem.
On de Broglie's quantum particle as the soliton solution of linear Schr?dinger equation  [PDF]
Agung Budiyono
Physics , 2007,
Abstract: We develop a class of soliton solution of {\it linear} Schr\"odinger equation without external potential. The quantum probability density generates its own boundary inside which there is internal vibration whose wave number is determined by the velocity of the particle as firstly conjectured by de Broglie. Assuming resonance of the internal vibration will lead to quantization of particle's momentum in term of wave number of the envelope quantum probability density. We further show that the linearity of the Schr\"odinger equation allows us to have non-interacting many solitons solution through superposition, each describing a particle with equal mass.
Universality  [PDF]
Emil Marinchev
Physics , 2002,
Abstract: This article is an attempt for a new vision of the basics of Physics, and of Relativity, in particular. A new generalized principle of inertia is proposed, as an universal principle, based on universality of the conservation laws, not depending on the metric geometry used. The second and the third principles of Newton's mechanics are interpreted as logical consequences. The generalization of the classical principle of relativity made by Einstein as the most basic postulate in the Relativity is criticized as logically not well-founded. A new theoretical scheme is proposed based on two basic principles: 1.The principle of universality of the conservation laws, and 2.The principle of the universal velocity. It is well- founded with examples of different fields of physics. Key words: Universality, New Insight in Physics
A de Broglie-Bohm Like Model for Dirac Equation  [PDF]
O. Chavoya-Aceves
Physics , 2003, DOI: 10.1393/ncb/i2003-10085-4
Abstract: A de Broglie-Bohm like model of Dirac equation, that leads to the correct Pauli equations for electrons and positrons in the low-speed limit, is presented. Under this theoretical framework, that affords an interpretation of the quantum potential, the main assumption of the de Broglie-Bohm theory--that the local momentum of particles is given by the gradient of the phase of the wave function--wont be accurate. Also, the number of particles wont be locally conserved. Furthermore, the representation of physical systems through wave functions wont be complete.
Developing de Broglie Wave  [PDF]
J X Zheng-Johansson,P-I Johansson
Physics , 2006,
Abstract: The electromagnetic component waves, comprising together with their generating oscillatory massless charge a material particle, will be Doppler shifted when the charge hence particle is in motion, with a velocity $v$, as a mere mechanical consequence of the source motion. We illustrate here that two such component waves generated in opposite directions and propagating at speed $c$ between walls in a one-dimensional box, superpose into a traveling beat wave of wavelength ${\mit\Lambda}_d$$=(\frac{v}{c}){\mit\Lambda}$ and phase velocity $c^2/v+v$ which resembles directly L. de Broglie's hypothetic phase wave. This phase wave in terms of transporting the particle mass at the speed $v$ and angular frequency ${\mit\Omega}_d=2\pi v /{\mit\Lambda}_d$, with ${\mit\Lambda}_d$ and ${\mit\Omega}_d$ obeying the de Broglie relations, represents a de Broglie wave. The standing-wave function of the de Broglie (phase) wave and its variables for particle dynamics in small geometries are equivalent to the eigen-state solutions to Schr\"odinger equation of an identical system.
The Universality of Einstein Equations  [PDF]
M. Ferraris,M. Francaviglia,I. Volovich
Physics , 1993, DOI: 10.1088/0264-9381/11/6/015
Abstract: It is shown that for a wide class of analytic Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of the so--called ``Palatini formalism'', i.e., treating the metric and the connection as independent variables, leads to ``universal'' equations. If the dimension $n$ of space--time is greater than two these universal equations are Einstein equations for a generic Lagrangian and are suitably replaced by other universal equations at bifurcation points. We show that bifurcations take place in particular for conformally invariant Lagrangians $L=R^{n/2} \sqrt g$ and prove that their solutions are conformally equivalent to solutions of Einstein equations. For 2--dimensional space--time we find instead that the universal equation is always the equation of constant scalar curvature; the connection in this case is a Weyl connection, containing the Levi--Civita connection of the metric and an additional vectorfield ensuing from conformal invariance. As an example, we investigate in detail some polynomial Lagrangians and discuss their bifurcations.
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