In this paper we consider normalizable time-periodic solutions of the Dirac equation in an extreme Kerr black hole background with massM and angular momentum J . We prove that for particular values of J and given azimuthal quantum number k the Dirac equation has a bound state solution, and the one-particle energy of this solution is given by ω = − 2J . Moreover, we present some necessary and su...

The quadratic form of the Dirac equation in a Riemann spacetime yields a gravitational gyromagnetic ratio κS = 2 for the interaction of a Dirac spinor with curvature. A gravitational gyromagnetic ratio κS = 1 is also found for the interaction of a vector field with curvature. It is shown that the Dirac equation in a curved background can be obtained as the square–root of the corresponding vecto...

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 (pspin) symmetry concept, we obtain the bound state energy spectra and the corresponding two-component upperand lower-spinors of the two Dirac particles by mean...

The Dirac equation is expressed entirely in terms of geometrical quantities by providing a geometrical interpretation for the (−1) which appears explicitly in the Dirac equation. In the modification of the Dirac electron theory which ensues, the (−1) appears as the generator of rotations in the spacelike plane orthogonal to the plane containing the electron current and spin vectors. This amount...

The article presents computer algebra procedures and routines applied to the study of the Dirac field on curved spacetimes. The main part of the procedures is devoted to the construction of Pauli and Dirac matrices algebra on an anholonomic orthonormal reference frame. Then these procedures are used to compute the Dirac equation on curved spacetimes in a sequence of special dedicated routines. ...

we describe how to obtain electronic transport properties of disordered graphene, including the tight binding model and nearest neighbor hopping. we present a new method for computing, electronic transport wave function and greens function of the disordered graphene. in this method, based on the small rectangular approximation, break up the potential barriers in to small parts. then using the f...

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...

(Abstract) The ordinary Schrödinger equation with minimal coupling for a nonrelativistic electron interacting with a single-mode photon field is not satisfied by the nonrelativistic limit of the exact solutions to the corresponding Dirac equation. A Schrödinger-like equation valid for arbitrary photon intensity is derived from the Dirac equation without the weak-field assumption. The ”eigenvalu...