Related papers: Lorentz-Dirac equation in the delta-function pulse
Exact solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic…
We solve the one-dimensional Dirac equation by taking into account the possibility of position-dependence in the mass function. We also take the Fermi velocity to act as a local variable and examine the combined effects of the two on the…
In this paper, we revisit the connection between the Riemann-Roch theorem and the zero energy solutions of the two-dimensional Dirac equation in the presence of a delta-function like magnetic field. Our main result is the resolution of a…
We consider the massless nonlinear Dirac (NLD) equation in $1+1$ dimension with scalar-scalar self-interaction $\frac{g^2}{2} (\bar{\Psi} \Psi)^2$ in the presence of three external electromagnetic potentials $V(x)$, a potential barrier, a…
We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice…
Mathematical justifications are given for several integral and series representations of the Dirac delta function which appear in the physics literature. These include integrals of products of Airy functions, and of Coulomb wave functions;…
In this paper, we describe the line Dirac delta function of a curve in three-dimensional space in terms of the distance function to the curve. Its extension to level set formulation and plane curves are also developed. The main ideas can be…
In this article we discuss the Dirac equation in the presence of an attractive cylindrical \delta-shell potential V(\rho)=-a\delta(\rho-\rho_0), where \rho is the radial coordinate and a>0. We present a detailed discussion on the boundary…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
Starting from an interpretation of the classical-quantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies…
We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzchild solution to an external, stationary electromagnetic Berttoti-Robinson solution. We separate the Dirac equation into radial and…
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…
After reviewing the algebraic derivation of the Doppler factor in the Lienard-Wiechert potentials of an electrically charged point particle, we conclude that the Dirac delta function used in electrodynamics must be the one obeying the weak…
We calculate correlation function in the Einstein--Podolsky--Rosen type of experiment with massive relativistic Dirac particles in the framework of the quantum field theory formalism. We perform our calculations for states which are…
We obtain solutions of the three dimensional Dirac equation for radial power-law potentials at rest mass energy as an infinite series of square integrable functions. These are written in terms of the confluent hypergeometric function and…
Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The found solutions are expressed in terms of new complex…
A motion of a classical free charge in an electromagnetic plane wave can be found exactly in a fully relativistic case. We have found an approximate non-parameter form of the suitable equations of motion. In a linearly polarized wave, in…
We introduced some contact potentials that can be written as a linear combination of the Dirac delta and its first derivative, the $\delta$-$\delta'$ interaction. After a simple general presentation in one dimension, we briefly discuss a…
The classical equation of motion of a charged point particle, including its radiation reaction, is described by the Lorentz-Dirac equation. We found a new class of solutions that describe tunneling (in a completely classical context!). For…
The Dirac delta function can be defined by the limitation of the rectangular function covering a unit area with decrease of the width of the rectangle to zero, and in quantum mechanics the eigenvectors of the position operator take the form…