Related papers: An algorithm for exact analytical solutions for ti…
The motion of a relativistic particle is linked to its spin by the Dirac equation. Remarkably, electrons in two-dimensional materials can mimic such Dirac particles but must always appear in pairs of opposite spin chirality. Using…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in the space of constant positive curvature, spherical Riemann space, in presence of an external magnetic field, analogue of the…
A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in…
We consider a Dirac electron in the presence of an exponentially decaying magnetic field. We obtain exact energy eigenvalues with a zero-energy state and the corresponding eigenfunctions. We also calculate the probability density and…
In this work we discuss the properties of the solutions of the Dirac equation in presence of an uniform background magnetic field. In particular we focus on the nature of the solutions, their ortho-normality properties and how these…
In this paper, one dimentional conformable fractional Dirac-type integro differential system is considered. The asymptotic formulae for the solutions, eigenvalues and nodal points are obtained. We investigate the inverse nodal problem and…
(Talk presented at the 7th Marcel Grossmann Meeting on General Relativity, Stanford, CA, July 24-30, 1994) We study the semi-classical limit of the solution of the Dirac equation in a background electromagnetic/gravitational plane wave. We…
The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the…
The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin…
Planar spin-transfer devices with dominating easy-plane anisotropy can be described by an effective one-dimensional equation for the in-plane angle. Such a description provides an intuitive qualitative understanding of the magnetic…
By employing an exponential-type approximation scheme to replace the centrifugal term, we have approximately solved the Dirac equation for spin- particle subject to the complex -symmetric scalar and vector P\"oschl-Teller (PT) potentials…
We solve a singe-particle Dirac equation with Woods-Saxon potentials using an iterative method in the coordinate space representation. By maximizing the expectation value of the inverse of the Dirac Hamiltonian, this method avoids the…
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time…
We review some recent results concerning lower eigenvalues estimates for the Dirac operator [6, 7]. We show that Friedrich's inequality can be improved via certain well-chosen symmetric tensors and provide an application to Sasakian spin…
We use the Dirac operator technique to establish sharp distance estimates for compact spin manifolds under lower bounds on the scalar curvature in the interior and on the mean curvature of the boundary. In the situations we consider, we…
We define (higher rank) spinorially twisted spin structures and deduce various curvature identites as well as estimates for the eigenvalues of the corresponding twisted Dirac operators.
We find an exact solution to the Dirac equation in 1-1 dimensional space-time in the presence of a time-dependent potential which consists of a combination of electric, scalar, and pseudoscalar terms.
It has been shown recently that Dirac operators satisfying the Ginsparg-Wilson relation provide a solution of the chirality problem in QCD at finite lattice spacing. We discuss different ways to construct these operators and their…
This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…
We show that the Dirac equation for real spinors can be naturally decomposed into a system of two first-order relativistic wave equations. The decomposition separates in a transparent way the real and imaginary parts of the Dirac equation…