Related papers: Periodic solutions for the Lorentz force equation …
The electrostatic force is described in this model by the action of electric dipole distributions on charged particles. The individual hypothetical dipoles are propagating at the speed of light in vacuum transferring momentum and energy…
We study equations for the mechanical movement of chains of identical particles in the plane interacting with their nearest-neighbors by bond stretching and by van der Waals and Coulomb forces. We find collinear and circular equilibria as…
We consider a physical model where the total energy is governed by surface tension and attractive screened Coulomb potential on the 3-dimensional space. We obtain different periodic equilibrium patterns i.e. stationary sets for this energy,…
Previous work on exact solutions has been shown that sources need to be appended to the field equation of Einstein's unified field theory in order to achieve physically meaningful results,such sources can be included in a variational…
In this work the existence of periodic solutions is studied for the Hamiltonian functions (Formula presented.) where the first term consist of a harmonic oscillator and the second term are homogeneous polynomials of degree 5 defined by two…
In this paper it is shown that the equations of electric field lines of an arbitrarily moving charged particle in the general case are reduced to homogeneous, linear differential equations with variable coefficients. For trajectories where…
Equation of motion of Sommerfeld sphere in the field of Coulomb center is numerically investigated. It is shown that contrary to Lorentz-Dirac equation in the attractive case there are physical solutions. In the repulsive case sphere gains…
Uniqueness results are established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell--Born--Infeld equations in boundary-free space under the condition that either the charge or current density…
For a relativistic charged particle moving in a constant electromagnetic field, its velocity 4-vector has been well studied. However, despite the fact that both the electromagnetic field and the equations of motion are purely real, the…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. Partial results obtained in a previous paper are completed to represent accurately…
The different types of orbits in the classical problem of two particles with equal masses and opposite charges on a plane under the influence of a constant orthogonal magnetic field are classified. The equations of the system are reduced to…
We discuss the motion of electrically and magnetically charged particles in the electromagnetic swirling universe. We show that the equations of motion can be decoupled in the Hamilton-Jacobi formalism, revealing the existence of a fourth…
The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion is confined to a two-dimensional plane,…
Periodically driven dynamics of a particle moving in the field Coulomb plus confining potential is treated for one and three dimensional cases. Critical value of the external field strength at which chaotization will occur is evaluated…
We propose a manifestly Lorentz covariant, non-commutative Dirac equation for charged particles interacting with an electromagnetic field. The equation is formulated on the operator level, but operators are not composed through the normal…
We show that the Lorentz force law, F^L_1=q_1(E+v_1xB) being the charge on particle 1 interacting with the electromagnetic fields due to all other particles, can be written in a pure field form F^L_1=-\nabla_1 U^{EM}. In this expression…
Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a…
Using the Mountain Pass Theorem, we establish the existence of periodic solution for Euler-Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part $K-W$ and a forcing term. We consider two…
In this paper we address the problem of a particle moving in singular one dimensional potentials in the framework of quantum mechanics with minimal length. Using the momentum space representation we solve exactly the Schrodinger equation…
The behaviour of a relativistic scalar particle in a possible scenario that arises from the violation of the Lorentz symmetry is investigated. The background of the Lorentz symmetry violation is defined by a tensor field that governs the…