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Discovery of electron hydrodynamics in graphene system has opened a new scope of analytic calculations in condensed matter physics, which was traditionally well cultivated in science and engineering as a non-relativistic hydrodynamics and…
In this work, we study the wave equations in 2D Euclidian space for a new non-central potential consisting of a Kratzer term and a dipole term. For Schrodinger equation, we obtain the analytical expressions of the energies and the wave…
We discuss the problem of the electron mass in the framework of Deformed Special Relativity (DSR), a generalization of Special Relativity based on a deformed Minkowski space (i.e. a four-dimensional space-time with metric coefficients…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
In this paper, we consider the Dirac-Coulomb equation for many-particles, to describe the interaction between electrons in the system having many electrons. The four-component wave function will expanding into a finite basis-set, using…
The electronic and magnetic properties of many strongly-correlated systems are controlled by a limited number of states, located near the Fermi level and well isolated from the rest of the spectrum. This opens a formal way for combining the…
Ionization of highly charged relativistic ions by neutral atoms and ions is considered. Numerical results of recently developed computer codes based on the relativistic Born and the equivalent-photon approximations are presented. The…
Electromagnetism is a \textit{relativistic} theory and one must exercise care in coupling this theory with \textit{nonrelativistic} classical mechanics and with \textit{nonrelativistic} classical statistical mechanics. Indeed historically,…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
The paper analyzes time propagation of Dirac observables - using Heisenberg representation - in the light of various pseudodifferential operator algebras (cf. [Co3], [Co15], [Co16]). Our theory gives (i) a mechanical angular momentum (the…
In this work, the calculation of complexity on atomic systems is considered. In order to unveil the increasing of this statistical magnitude with the atomic number due to the relativistic effects, recently reported in [A. Borgoo, F. De…
This work derives exact solutions to the problem of interacting particle density evolution in relativistic and quasi-relativistic approximations for electromagnetic and gravitational interactions. Two types of radial symmetry for the…
A fourth-order Schr\"{o}dinger equation for the description of charge transport in semiconductors in the ballistic regime is proposed with the inclusion of non-parabolic effects in the dispersion relation in order to go beyond the simple…
Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic…
We reexamine the model of relativistic particle with higher-derivative term linear on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here.…
Electrons in solids are characterized by the energy bands, which indicate that electrons are considered to be "elementary particles" with specific effective masses and g-factors reflecting features of each solid. There are cases where these…
Relativistic calculations of the electronic structure of the superheavy element of the eighth period $-$ eka-francium ($Z=119$) and its homologues, which form the group of alkali metals, are performed in the framework of the…
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…
Relativistic treatments of quantum mechanical systems are important for understanding hadronic structure and dynamics at sub-nucleon distance scales. Hadronic states in different inertial reference frames are needed to compute current…
Schrodinger equation with two-component wave function which describes a relativistic spin 1/2 particle in a weak electromagnetic field is obtained. In the same approximation Schrodinger equation with traditional norm condition and…