Related papers: Analytical solutions of the Dirac equation using t…

Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…

We obtain exact solutions of Dirac equation at zero kinetic energy for radial power-law relativistic potentials. It turns out that these are the relativistic extension of a subclass of exact solutions of Schrodinger equation with two-term…

We define and study the probability current and the Hamiltonian operator for a fully general set of Dirac matrices in a flat spacetime with affine coordinates, by using the Bargmann-Pauli hermitizing matrix. We find that with some weak…

The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows to recover quantum mechanics as mechanics on a non-differentiable (fractal) space-time. The…

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…

We consider the problem of resolving all pairwise interactions of shock waves, contact waves, and rarefaction waves in 1-dimensional flow of an ideal polytropic gas. Resolving an interaction means here to determine the types of the three…

We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field. In order to describe the corresponding structure, we consider the propagation of…

In previous publications, we illustrated the effectiveness of the method of the inhomogeneous differential equation in calculating the electric polarizability in the one-dimensional problem. In this paper we extend our effort to apply the…

In this paper, we introduce an extension of the Dirac equation, very similar to Dirac oscillator, that gives stationary localized wave packets as eigenstates of the equation. The extension to the Dirac equation is achieved through the…

In this paper, we solve the initial value problems of variable-coefficient generalized wave equations associated with trees and a large family of linear constant-coefficient partial differential equation by algebraic methods. Moreover, we…

An exact solution is obtained for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene. The graphene is represented by an infinitesimally-thin, local and isotropic two-sided…

The behavior of electrons in strained graphene is usually described using effective pseudomagnetic fields in a Dirac equation. Here we consider the particular case of a spatially constant strain. Our results indicate that lattice…

The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic properties of a tense membrane of graphene are considered within a non-perturbative approach, leading to an electron-ripple coupling. The…

Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of…

We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…

In this pedagogical paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d…

The relativistic wave equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave, in a medium of index of refraction n_m < 1, have been studied. In the Dirac case the found exact solutions…

In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…

The Dirac equation is invariant under rotations with a constant frequency and invariable cylindrical radius. 3D transformation for rotating frames is found with help of this invariance. Exact localized solutions of the Dirac equation in the…

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…