Related papers: General solution of the Dirac equation for quasi-t…
We describe a new class of exact square integrable solutions of the Pauli and Dirac equation in rotating electromagnetic fields. Solutions obtained by putting equations in the stationary form with help of a coordinate transformation…
The energy relaxation in the spin-polarized disordered electron systems is studied in the diffusive regime. We derived the quantum kinetic equation in which the kernel of electron-electron collision integral explicitly depends on the…
Closed-form, normalizable solutions of Dirac's equation propagating within a semi-infinite cylindrical waveguide are obtained in terms of ordinary and modified Bessel functions. These relativistic wave packets induce quantum backflow on a…
We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.
Based on the results of F. Wilf on the need to take into account the quantum-mechanical correspondence rules in the Dirac equation for an electron, it was shown that the equation obtained by giving physical meaning to $\alpha$-Dirac…
In this article we present a detailed description of an electron in a uniform magnetic field evolving under the Schr\"odinger equation using ladder operators. Based on this analysis, we describe the same physical system using the Dirac…
Energies and wave functions are calculated for d-wave quasiparticles in the mixed state using the formalism of Franz and Tesanovic for the low-lying energy levels. The accuracy of the plane-wave expansion is explored by comparing…
The late time asymptotics of the physical solutions to the Lorentz-Dirac equation in the electromagnetic external fields of simple configurations -- the constant homogeneous field, the linearly polarized plane wave (in particular, the…
In this work we provide a novel class of degenerate solutions to the Dirac equation for massive particles, where the rotation of the spin of the particles is synchronized with the rotation of the magnetic field of the wave-like…
The usual method of solving the free particle Dirac equation results in the so called continuum energy solutions. Here, we take a different approach and find a set of solutions with quantized energies which are proportional to the total…
We obtain exact solution of the Dirac equation with the Coulomb potential as an infinite series of square integrable functions. This solution is for all energies, the discrete as well as the continuous. The spinor basis elements are written…
We show that the energy spectrum of the one-dimensional Dirac equation in the presence of a spatial confining point interaction exhibits a resonant behavior when one includes a weak electric field. After solving the Dirac equation in terms…
It was known that a free, nonrelativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current --- hence termed quantum backflow. Here, it is shown that more variations can be brought…
We report measurements of the spin susceptibility in dilute two-dimensional electrons confined to a 45$\AA$ wide AlAs quantum well. The electrons in this well occupy an out-of-plane conduction-band valley, rendering a system similar to…
By analyzing the Dirac equation with static electric and magnetic fields it is shown that Dirac's theory is nothing but a generalized one-particle quantum theory compatible with the special theory of relativity. This equation describes a…
The Dirac equation, in the field of a traveling circularly polarized electromagnetic wave and a constant magnetic field, has singular solutions, corresponding the expansion of energy in vicinity of some singular point. These solutions…
In this paper we obtain exact solutions of a 2D relativistic Dirac oscillator in the presence of a constant magnetic field. We compute the energy spectrum and discuss its dependence on the spin and magnetic field strength.
Coupling of spin states and space motion of conduction electrons due to spin-orbit interaction opens up possibilities for manipulation of the electron spins by electrical means. It is shown here that spin orientation of a two-dimensional…
We formulate the Dirac equation for a massive neutral spin-half particle on a rotating black hole spacetime, and we consider its (quasi)bound states: gravitationally-trapped modes which are regular across the future event horizon. These…
It is demonstrated that in a two--band 2D system the resonance state is manifested close to the energy of the Dirac point in the electron spectrum for the sufficiently large impurity perturbation. With increasing the impurity concentration,…