Related papers: Equivalence of Two Methods to Solve Static Electro…
A procedure for solving the Maxwell equations in vacuum, under the additional requirement that both scalar invariants are equal to zero, is presented. Such a field is usually called a null electromagnetic field. Based on the complex Euler…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
In this manuscript, we investigate the exact bound state solution of the Klein-Gordon equation for an energy-dependent Coulomb-like vector plus scalar potential energies. To the best of our knowledge, this problem is examined in literature…
The propagator and complete sets of in- and out-solutions of wave equation, together with Bogoliubov coefficients, relating these solutions, are obtained for vector $W$-boson (with gyromagnetic ratio $g=2$) in a constant electromagnetic…
The Biot-Savart law is a well-known and powerful theoretical tool used to calculate magnetic fields due to currents in magnetostatics. We extend the range of applicability and the formal structure of the Biot-Savart law to electrostatics by…
We present an analytical strategy to solve the electric field generated by a planar region $\mathcal{A}$ enclosed by a contour $c$ which is kept with a fixed but non-uniform electric potential. The approach can be used in certain situations…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After…
The action of certain static magnetic fields on charged test particles is interpreted as a consequence of the interaction of the particles with electric dipole distributions emitted by other charged particles in relative motion. The dipole…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
A novel soliton-like solution in quantum electrodynamics is obtained via a self-consistent field method. By writing the Hamiltonian of quantum electrodynamics in the Coulomb gauge, we separate out a classical component in the density…
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into…
It is shown that the well-known procedure for proving the equivalence of the expressions for the electric field calculated using the Lorentz and Coulomb gauges is incorrect. The difference between the two gauges is due to the difference in…
Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of electrolyte can then be treated as a composite non-uniform…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…
Vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The rapid development in quantum optics calls for electromagnetic solutions that straddle quantum physics as well as classical physics. The…
The exact solutions of the equation for a composite scalar particle which possesses electric and magnetic polarizabilities are found in an external uniform static magnetic field parallel to the direction of propagation of the quantized…
We present derivations of the expressions for the spherical volume averages of static electric and magnetic fields that are virtually identical. These derivations utilize the Coulomb and Biot-Savart laws, and make no use of vector calculus…
We consider a coupled system of Navier-Stokes and Nernst-Planck equations, describing the evolution of the velocity and the concentration fields of dissolved constituents in an electrolyte solution. Motivated by recent applications in the…
In preparation to the exascale era, an alternative approach to calculate the electrostatic forces in Particle Mesh (PM) methods is proposed. While the traditional techniques are based on the calculation of the electrostatic potential by…