Related papers: Spin 0 and spin 1/2 quantum relativistic particles…
We study the Klein-Gordon and Dirac equations in the presence of a background metric ds^2 = -dt^2 + dx^2 + e^{-2gx}(dy^2 + dz^2) in a semi-infinite lab (x>0). This metric has a constant scalar curvature R=6g^2 and is produced by a perfect…
A relativistic particle in an attractive Coulomb field as well as a static and spherically symmetric gravitational field is studied. The gravitational field is treated perturbatively and the energy levels are obtained for both spin 0…
The Klein-Gordon and Dirac equations are considered in a semi-infinite lab ($x > 0$) in the presence of background metrics $ds^2 =u^2(x) \eta_{\mu\nu} dx^\mu dx^\nu$ and $ds^2=-dt^2+u^2(x)\eta_{ij}dx^i dx^j$ with $u(x)=e^{\pm gx}$. These…
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…
Spin-1/2 particles can be used to study inertial and gravitational effects by means of interferometers, particle accelerators, and ultimately quantum systems. These studies require, in general, knowledge of the Hamiltonian and of the…
We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar…
Klein-Gordon and Dirac equations are the motion equations for relativistic particles with spin 0 (so-called scalar particles) and 1/2 (electron/positron) respectively. For a free particle, the Dirac equation is derived from the Klein-Gordon…
In this article, we investigate the relativistic quantum dynamics of spin-$\frac{1}{2}$ particles in (1+2)-dimensional G\"{u}rses space-time backgrounds, and analyze the effects on the eigenvalues. We solve the Dirac equation using the…
The relativistic wave equation for spin-1/2 particles in the interior Schwarzschild solution in the presence of a uniform magnetic field is obtained. The fully relativistic regime is considered, and the energy levels occupied by 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,…
The Dirac equation for massive free electrically neutral spin 1/2 particles in a gravitation field is considered. The secondary quantization procedure is applied to it and the Hilbert space of multiparticle quantum states is constructed.
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…
In this paper, the principles of the general relativity are used to formulate quantum wave equations for spin-0 and spin-1/2 particles. More specifically, the equations are worked in a Schwarzschild-like metric. As a test, the hydrogen atom…
Requiring covariance of Maxwell's equations without {\it a priori} imposing charge invariance allows for both spin-1 and spin-1/2 transformations of the complete Maxwell field and current. The spin-1/2 case yields new transformation rules,…
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential…
The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic…
In the present study, Kummer's eigenvalue spectra from a charged spinless particle located at spherical pseudo-dot of the form $r^2+1/r^2$ is reported. Here, it is shown how confluent hypergeometric functions have principal quantum numbers…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…
Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of…
We study the Dirac oscillator for spin-1/2 particles in a spacetime containing a spinning cosmic string endowed with both curvature (disclination) and torsion (screw dislocation). The background geometry includes off-diagonal and is…