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The generalised Boltzmann equation which treats the combined localised and delocalised nature of transport present in certain materials is extended to accommodate time-dependent fields. In particular, AC fields are shown to be a means to…
We study the dynamics of an electron wave packet in a strong constant crossed electromagnetic field with account for radiative corrections due to interaction of the electron with the vacuum fluctuations. We evaluate a wave packet composed…
There are important differences between the nonrelativistic and relativistic description of electron beams. The orbital angular momentum quantum number cannot be used to specify the wave functions in the relativistic case. In this Letter we…
Electrons in materials containing heavy elements are fundamentally relativistic and should in principle be described using the Dirac equation. However, the current standard for treatment of electrons in such materials involves density…
Maxwell's equations and the Dirac equation are the first-order differential relativistic wave equation for electromagnetic waves and electronic waves respectively. Hence, there is a notable similarity between these two wave equations, which…
Dirac's equation of the electron will be discussed by using quaternions as the basis of a new formalism which seems to be very well adapted to the problem. The transformation properties of the equations as well as the invariant and…
In this manuscript, we study the relativistic quantum mechanics of an electron in external fields in the spinning cosmic string spacetime. We obtain the Dirac equation, write the first and second-order equations from it, and then we solve…
The electron's spin magnetic moment is ordinarily described as anomalous in comparison to what one would expect from the Dirac equation. But, what exactly should one expect from the Dirac equation? The standard answer would be the Bohr…
In this contribution we study the Dirac equation for a finite size proton in an external electric field with explicit introduction of Dirac-Pauli form factors. Our aim is twofold. On the one hand, we wish to study whether our conclusions…
A theoretical study of the intense-field multiphoton ionization of hydrogenlike systems is performed by solving the time-dependent Dirac equation within the dipole approximation. It is shown that the velocity-gauge results agree to the ones…
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…
The Dirac equation is used to describe oblique spin-conserving and spin-flip reflections of relativistic electrons from a one-dimensional potential barrier in a vacuum. When an electron hits the barrier from an oblique direction, its…
We study in the framework of relativistic quantum mechanics the evolution of a system of two Dirac neutrinos that mix with each other and have non-vanishing magnetic moments. The dynamics of this system in an external magnetic field is…
Boundary-dependent radiative corrections that modify the magnetic moment of an electron near a dielectric or conducting surface are investigated. Normal-mode quantization of the electromagnetic field and perturbation theory applied to 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 Hamiltonian formulation of the motion of a spinning relativistic particle in an external electromagnetic field is considered. The approach is based on the introduction of new coordinates and their conjugated momenta to describe the spin…
The time-dependent Dirac equation is solved using the three-dimensional Finite Difference-Time Domain (FDTD) method. The dynamics of the electron wave packet in a vector potential is studied in the arrangements associated with the…
The exact solution of the Dirac equation and the spectrum of electron quasi-energies in a superposition of the field of a circularly polarized electromagnetic wave and a homogeneous magnetic field parallel to the direction of wave…
All known solutions of the Dirac equation describing states of electrons endowed with angular momentum are very far from our notion of the electron as a spinning charged bullet because they are not localized in the direction of propagation.…
We prove a sharp-in-time dispersive estimate of the Dirac equation on spinor bundles over the real hyperbolic space. Compared with the Euclidean counterparts, our result shows that the dispersive estimate differs between short and long…