Treating some solid state problems with the Dirac equation

Some extensions of the Einstein-Dirac Equation

We considered an extension of the standard functional for the Einstein-Dirac equation where the Dirac operator is replaced by the square of the Dirac operator and a real parameter controlling the length of spinors is introduced. For one distinguished value of the parameter, the resulting Euler-Lagrange equations provide a new type of EinsteinDirac coupling. We establish a special method for con...

The Modified Dirac Equation

We consider the behavior of particles at ultra relativistic energies, for both the Klein-Gordon and Dirac equations. We observe that the usual description is valid for energies such that we are outside the particle’s Compton wavelength. For higher energies however, both the Klein-Gordon and Dirac equations get modified and this leads to some new effects for the particles, including the appearan...

The Lorentz - Dirac equation

The Lorentz-Dirac equation (LDE) x 000 ? x 00 = d dx V (x) models the point limit of the Maxwell-Lorentz equation describing the interaction of a charged extended particle with the electromagnetic eld. Since (LDE) admits solutions which accelerate even if they are outside the zone of interaction, Dirac proposed to study so-called "non runaway" solutions satisfying the condition x 00 (t) ! 0 as ...

Linear and Nonlinear Dirac Equation: advances and open problems

Approximate bound states of the Dirac equation with some physical quantum potentials

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...