Related papers: From Fermat Principle to Wave equation
Motivated by a revision of the classical equations of electromagnetism that allow for the inclusion of solitary waves in the solution space, the material collected in these notes examines the consequences of adopting the modified model in…
The transformation converting equations invariant under Lorentz into the equations invariant under Galileo is obtained. On this basis: (1) the super-light electromagnetic wave with longitudinal and transversal modes is found out; (2) it is…
There are many papers devoted to derivation of Lorentz Transformations (LT). Many people have pro posed alternative derivations. Their analysis allows looking at LT and their consequences from different standpoints. At the same time it is…
The least action principle is established for the dynamics of a test particle in a dilaton-Maxwell background. These dynamics and background are invariant under the action of the dilatation transformation; explicit form of the corresponding…
On the basis of the relativistic symmetry of Minkowski space, we derive a Lorentz invariant equation for a spread electron. This equation slightly differs from the Dirac equation and includes additional terms originating from the spread of…
Relativistically covariant equation of motion for real dust particle under the action of electromagnetic radiation is derived. The particle is neutral in charge. Equation of motion is expressed in terms of particle's optical properties,…
The concept of matter wave radiation is put forward, and its equation is established for the first time. The formalism solution shows that the probability density is a function of displacement and time. A free particle and a two-level…
New method of quantization is presented. It is based on classical Newton-Lagrange equations of motion (representing the fundamental physical law of mechanics) rather than on their traditional Lagrangian and/or Hamiltonian precursors. It is…
For the electromagnetic interaction of two particles the relativistic quantum mechanics equations are proposed. These equations are solved for the case when one particle has a small mass and moves freely. The initial wave functions are…
One propose a relativistic version of the transfer matrix method for an electron moving through a given number of rectangular barriers of arbitrary shape. It is shown that starting with the Dirac equation depending on the effective mass and…
A brief review of the different ways of the Dirac equation derivation is given. The foundations of the relativistic canonical quantum mechanics of a fermionic doublet are formulated. In our approach the Dirac equation is derived from the…
Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or…
It is currently believed that light quantum or the quantization of light energy is beyond classical physics and the picture of wave-particle duality, which was criticized by Einstein but attracted a number of experimental researches, is…
The dynamics of a radiating charge is one of the oldest unsettled problems in classical physics. The standard Lorentz-Abraham-Dirac (LAD) equation of motion is known to suffer from several pathologies and ambiguities. This paper briefly…
We prove that the field equations of general relativity and other metric theories can be derived from the conservation of energy-momentum without using the assumption of least action principle. We show a new procedure for perturbative…
Mathematical models for the stochastic evolution of wave functions that combine the unitary evolution according to the Schroedinger equation and the collapse postulate of quantum theory are well understood for non-relativistic quantum…
This chapter derives the properties of light from the properties of processing, including its ability to be both a wave and a particle, to respond to objects it doesn't physically touch, to take all paths to a destination, to choose a route…
A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…
In this article, it is suggested that a pedagogical point of departure in the teaching of classical mechanics is the Liouville theorem. The theorem is interpreted to define the condition that describe the conservation of information in…
In the 17th and 18th centuries, several natural philosophers studied the phenomenon of refraction and attempted to obtain the Snell law from various assumptions. Lacking experimental data, it was generally believed that light travels faster…