Related papers: The Dirac Equation in (1+2)-dimensional G\"{u}rses…
The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal…
In this paper, we study the relativistic quantum problem of a particle constrained to a double cone surface. For this purpose, we build the Dirac equation in a curved space using the tetrads formalism. Two cases are analysed. First, we…
In this article, we study the DKP equation for the oscillator in a G\"{o}del-type space-time background. We derive the final form of this equation in a flat class of G\"{o}del-type space-time and solve it analytically, and evaluate the…
In this paper, our focus is on investigating the impact of cosmological constant on relativistic quantum systems comprising spin-0 scalar particles. Our analysis centers around the Klein-Gordon equation, and we obtain both approximate and…
We present exact solutions of the Dirac equation in static curved space-time using two distinct algebraic approaches. The first method employs $su(1,1)$ algebra operators together with the tilting transformation, enabling the derivation of…
The Klein-Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, $V_{v}=V_{s} + \mathrm{const.}$ These isospectral problems are solved in a case of squared trigonometric potential…
In this work the dynamics of a 2D Dirac oscillator in the spacetime of a magnetic cosmic string is considered. It is shown that earlier approaches to this problem have neglected a $\delta$ function contribution to the full Hamiltonian,…
The relativistic two-body system in (1+1)-dimensional quantum electrodynamics is studied. It is proved that the eigenvalue problem for the two-body Hamiltonian without the self-interaction terms reduces to the problem of solving an…
We study the relativistic quantum dynamics of spin-$0$ massive charged particle in a G\"{o}del-type space-time with electromagnetic interactions. We solve the Klein-Gordon equation subject to a uniform magnetic field in the Som-Raychaudhuri…
The core concept of quantum simulation is the mapping of an inaccessible quantum system onto a controllable one by identifying analogous dynamics. We map the Dirac equation of relativistic quantum mechanics in 3+1 dimensions onto a…
Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.
We approximately solve the Dirac equation for the inversely quadratic Yukawa (IQY) potential including a Coulomb-like tensor potential with arbitrary spin-orbit coupling quantum number . In the framework of the spin and pseudospin (pspin)…
We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in…
In this paper we solve analytically Dirac equation for Eckart plus Hulthen potentials with Coulomb-like and Yukawa-like tensor interaction in the presence of Spin and Pseudo-spin Symmetry for any k number. The Parametric Nikiforov-Uvarov…
This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to…
The gravitational couplings of intrinsic spin are briefly reviewed. A consequence of the Dirac equation in the exterior gravitational field of a rotating mass is considered in detail, namely, the difference in the energy of a spin-1/2…
The role of the Hulthen potential on the spin and pseudospin symmetry solutions is investigated systematically by solving the Dirac equation with attractive scalar S(r) and repulsive vector V(r) potentials. The spin and pseudospin symmetry…
Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
A new method for solving the time-dependent two-center Dirac equation is developed. The time-dependent Dirac wave function is represented as a sum of atomic-like Dirac-Sturm orbitals, localized at the ions. The atomic orbitals are obtained…