Related papers: Dirac Equations with Confining Potentials
We present a systematic approach for the separation of variables for the two-dimensional Dirac equation in polar coordinates. The three vector potential, which couple to the Dirac spinor via minimal coupling, along with the scalar potential…
We investigate the relativistic effects of a moving particle in the field of a pseudo-harmonic oscillatory ring-shaped potential under the spin and pseudo-spin symmetric Dirac wave equation. We obtain the bound state energy eigenvalue…
The "spin-up" and "spin-down" projections of the second order, chiral form of Dirac Theory are shown to fit a superposition of forms predicted in an earlier classical, complex scalar gauge theory (April, 1992 Class. Quantum Grav.). In some…
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of…
The Thomas-Bargmann-Michel-Telegdi (T-BMT) equation is derived using the Exact Foldy-Wouthuysen transformation. Extra new terms were found, and we discuss their possible physical applications. The main point of this work is to detail the…
We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb operator in a suitable complete square integrable basis. Orthogonal polynomials techniques along with Darboux method are used to obtain the bound states energy…
We propose a mathematical model of \textit{quantum} transistor in which bandgap engineering corresponds to the tuning of Dirac potential in the complex four-vector form. The transistor consists of $n$-relativistic spin qubits moving in…
We report the implementation of effective QED potentials for all-electron 4-component relativistic molecular calculations using the DIRAC code. The potentials are also available for 2-component calculations, proper picture-change being…
Two Body Dirac Equations (TBDE) of Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. Coulomb-type potentials in these applications lead…
The paper is concerned with the following $n\times n$ Dirac type equation$$Ly=-iB(x)^{-1}(y'+Q(x)y)=\lambda y, \quad B(x)=B(x)^*,\quad y={\rm col}(y_1,\ldots,y_n),\quad x\in[0,\ell],$$ on a finite interval $[0,\ell]$. Here $Q$ is a summable…
A computational method is proposed to calculate bound and resonant states by solving the Klein-Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential…
The spin 1 particle is treated in the presence of the Dirac magnetic monopole in the Minkowski and Lobachevsky spaces. Separating the variables in the frame of the matrix 10-component Duffin-Kemer-Petiau approach (wave equation) and making…
The Dirac equation for an electron in a finite dipole potential has been studied within the method of linear combination of atomic orbitals (LCAO). The Coulomb potential of the nuclei that compose a dipole is regularized, by considering the…
In the semiclassical approximation of Grassmann-valued electric charges for regularizing Coulomb self-energies, we extract the unique acceleration-independent interaction hidden in any Lienard-Wiechert solution for the system of N…
Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the…
In the literature of calculating atomic and molecular structures, most Schrodinger equations are described by Coulomb potential. However, there are also a few literatures that discuss some magnetic correction methods, such as Pauli and…
The theory of entropic gravity conjectures that gravity emerges thermodynamically rather than being a fundamental force. One of the main criticisms of entropic gravity is that it would lead to quantum massive particles losing coherence in…
We propose and study the properties of a non-linear electrodynamics that emerges inspired on the physics of Dirac materials. This new electrodynamic model is an extension of the one-loop corrected non-linear effective Lagrangian computed in…
Ponderomotive energy shifts experienced by Rydberg atoms in optical fields are known to be well approximated by the classical quiver energy of a free electron. We examine such energy shifts quantum mechanically and elucidate how they relate…
Three-dimensional quantum electrodynamics exhibits a number of interesting properties, such as dynamical chiral symmetry breaking, weak confinement, and non-Fermi liquid behavior, and also has wide applications in condensed matter physics.…