Related papers: General solution of the Dirac equation for quasi-t…
We present exact analytical solutions of the Dirac equation in $(1+1)$-dimensions for the generalized Kratzer potential by taking the pseudoscalar interaction term as an attractive Coulomb potential. We study the problem for a particular…
We consider quantum rings realized in materials where the dynamics of charge carriers mimics that of two-dimensional (2D) Dirac electrons. A general theoretical description of the ring-subband structure is developed that applies to a range…
The recent literature shows a renewed interest, with various independent approaches, in the classical theories for spin. Considering the possible interest of those results, at least for the electron case, we purpose in this paper to explore…
We discuss the generalization of the Dirac equations and spinors in momentum space to free unstable spin-$1/2$ fermions taking into account the fundamental requirement of Lorentz covariance. We derive the generalized adjoint Dirac equations…
We present the exact wave functions and energy levels of electron in a two-dimensional circular quantum dot in the presence of the Rashba spin-orbit interaction. The confinement is described by the realistic potential well of finite depth.
We address the behavior of the Dirac equation with the Killingbeck radial potential including the external magnetic and Aharonov-Bohm (AB) flux fields. The spin and pseudo-spin symmetries are considered. The correct bound state spectra and…
A non-perturbative approach to the solution of the time-dependent, two-center Dirac equation is presented with a special emphasis on the proper treatment of the potential of the nuclei. In order to account for the full multipole expansion…
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 spin relaxation of a two-dimensional electron system (2DES) formed in a symmetric quantum well is studied theoretically when the quantum well is parallel to the (110) plane of the zinc-blende structure, the spin polarization is…
We present a general procedure for determining quasi-exact solvability of the Dirac and the Pauli equation with an underlying $sl(2)$ symmetry. This procedure makes full use of the close connection between quasi-exactly solvable systems and…
The bound state (energy spectrum and two-spinor wave functions) solutions of the Dirac equation with the Hulthen potential for all angular momenta based on the spin and pseudospin symmetry are obtained. The parametric generalization of the…
Dynamic response of two-dimensional electron systems with spin-orbit interaction is studied theoretically on the basis of quantum kinetic equation, taking into account elastic scattering of electrons. The spin polarization and spin current…
A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell's equations, which yield a desired evolution. In particular, we show…
A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed. The obtained general quantum-mechanical solution of the relativistic paraxial equation contains the commonly accepted result as a…
The Relativistic Dynamical Inversion technique, a novel tool for finding analytical solutions to the Dirac equation, is written in explicitly covariant form. It is then shown how the technique can be used to make a change from Cartesian to…
Solution of the Dirac equation predicts that when an electron with non-zero orbital angular momentum propagates in a cylindrically symmetric potential, its spin and orbital degrees of freedom interact, causing the electron's phase velocity…
We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in $D$ dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first…
We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term…
We study the Dirac equation minimally coupled to general relativity using quantum field theory and the semiclassical gravity approximation. Previous studies of the Einstein-Dirac system did not quantize the Dirac field and required multiple…
We build the fully relativistic quantum field theory related to the asymmetric Dirac fields. These fields are solutions of the asymmetric Dirac equation, a Lorentz covariant Dirac-like equation whose positive and "negative" frequency plane…