Related papers: Solutions of the Dirac equation in one-dimensional…
This paper offers educational insight into the Dirac equation, examining its historical context and contrasting it with the earlier Schr\"odinger and Klein-Gordon (KG) equations. The comparison highlights their Lorentz transformation…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in the space of constant positive curvature, spherical Riemann space, in presence of an external magnetic field, analogue of the…
We consider the model of Dirac fermions coupled to gravity as proposed in \cite{VolovikBH}, in which superluminal velocities of particles are admitted. In this model an extra term is added to the conventional Hamiltonian that originates…
The Dirac equation is generalized to $D+1$ space-time.The conserved angular momentum operators and their quantum numbers are discussed. The eigenfunctions of the total angular momenta are calculated for both odd $D$ and even $D$ cases. The…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
In this letter, we consider a Schrodinger equation for a well potential with varying width. We solve one dimensional time-dependent Schrodinger equation subject to time-dependent boundary conditions for a spinless particle inside infinite…
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…
We derive and solve the Hamiltonian flow equations for a Dirac particle in an external static potential. The method shows a general procedure for the set up of continuous unitary transformations to reduce the Hamiltonian to a quasidiagonal…
We study the quantum behaviour of a particle moving in a one-dimensional double well potential. This double well is obtained by gluing together, at the origin, two shifted harmonic oscillator potentials. The Schr\"odinger equation is…
We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzchild solution to an external, stationary electromagnetic Berttoti-Robinson solution. We separate the Dirac equation into radial and…
We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the…
Presented is a quantum computing representation of Dirac particle dynamics. The approach employs an operator splitting method that is an analytically closed-form product decomposition of the unitary evolution operator. This allows the Dirac…
In this paper, a simple method is proposed to get analytical solutions (or with the help of a finite numerical calculations) of the Dirac-Weyl equation for low energy electrons in graphene in the presence of certain electric and magnetic…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
We analyze possible motion control of microparticles by means of external electromagnetic fields which induce potential wells having fixed spatial distribution but deepening over time up to some limit. It is assumed that given particles are…
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…
We solve the single particle Dirac bound state equation with a particular confining potential and comment its significance from the point of view of the quantum field theory. We show that the solutions describe a complex physical system…
The emergence of the concept of a causal fermion system is revisited and further investigated for the vacuum Dirac equation in Minkowski space. After a brief recap of the Dirac equation and its solution space, in order to allow for the…
In terms of the relational approach to space-time geometry and physical interactions, we show that the Dirac equation for a free fermion in the momentum representation can be obtained starting from a binary system of complex relations…
The Dirac equation is considered with the recently proposed generalized gravitational interaction (Kepler or Coulomb), which includes post-Newtonian (relativistic) and quantum corrections to the classical potential. The general idea in…