Related papers: The Dirac Equation in (1+2)-dimensional G\"{u}rses…
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…
I investigate the quantum dynamics of a spin-$1/2$ particle in a static, spherically symmetric Einstein-Gauss-Bonnet (EGB) black-hole spacetime within the Hamiltonian framework. Starting from the Dirac equation in curved spacetime,…
We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice…
The eigenvalues of the Dirac operator on a curved spacetime are diffeomorphism-invariant functions of the geometry. They form an infinite set of ``observables'' for general relativity. Recent work of Chamseddine and Connes suggests that…
The solvability of The Dirac equation is studied for the exponential-type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov-Uvarov method. The energy eigenvalue equation, and the corresponding…
Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, Wei Hua potential and Varshni potential with any $\kappa$-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed…
The equation of the spin-$\frac{1}{2}$ particles in the Friedmann-Lema\^itre-Robertson-Walker spacetime is investigated. The retarded and advanced fundamental solutions to the Dirac operator and generalized Dirac operator as well as the…
In the present article we have found the complete energy spectrum and the corresponding eigenfunctions of the Dirac oscillator in two spatial dimensions. We show that the energy spectrum depends on the spin of the Dirac particle.
Many calculations in strong field quantum field theory are carried out by using a simple field geometry, often neglecting the spacial field envelope. In this article, we simulate the electron diffraction quantum dynamics of the…
Using the Newman-Penrose formalism we calculate the positive energy momentum eigenstates of the Dirac equation for a plane polarized grav- itational wave pulse. We then consider Dirac particles whose spins are polarized in each orthonormal…
A pedagogical introduction to the Dirac equation for massive particles in Rindler space is presented. The spin connection coefficients are explicitly derived using techniques from general relativity. We then apply the Lagrange-Green…
Dirac equation is solved for some exponential potentials, hypergeometric-type potential, generalized Morse potential and Poschl-Teller potential with any spin-orbit quantum number $\kappa$ in the case of spin and pseudospin symmetry,…
In this work, we investigate the relativistic quantum dynamics of spin-0 massive charged particles in a 4D curved space-time, the generalization of a cosmic string space-time. We investigate the Klein-Gordon equation in the presence of…
Quantum dynamics of a Dirac particle in a 1D box with moving wall is studied. Dirac equation with time-dependent boundary condition is mapped onto that with static one, but with time-dependent mass. Exact analytical solution of such…
A relativistic wave equation for spin 1/2 particles in the Melvin space-time, a space-time where the metric is determined by a magnectic field, is obtained. The effects of very intense magnetic fields in the energy levels, as intense as the…
The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin…
The aim of this work is to find exact solutions of the Dirac equation in 1+1 space-time beyond the already known class. We consider exact spin (and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus (and…
The Dirac equation is a cornerstone in the history of physics, merging successfully quantum mechanics with special relativity, providing a natural description of the electron spin and predicting the existence of anti-matter. Furthermore, it…
In this paper we study the (2 + 1)-dimensional Dirac oscillator in the noncommutative phase space and the energy eigenvalues and the corresponding wave functions of the system are obtained through the sl(2) algebraization. It is shown that…
Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer Duffin equations for particles of…