In this paper we analyze the relativistic quantum motion of charged spin-0 and spin-
 $\frac{1}{2}$
 particles in the presence of a uniform magnetic field and scalar potentials in the cosmic string spacetime. In order to develop this analysis, we assume that the magnetic field is parallel to the string and the scalar potentials present a cylindrical symmetry with their center on the string. Two distinct configurations for the scalar potential, S(r), are considered: (i) the potential proportional to the inverse of the polar distance, i.e., S∝1/r, and (ii) the potential proportional to this distance, i.e., S∝r. The energy spectra are explicitly computed for different physical situations and their dependences on the magnetic field strength and scalar coupling constants are presented.

Relativistic quantum dynamics of a charged particle in cosmic string spacetime in the presence of magnetic field and scalar potential

Particle penetration through a square potential barrier is studied with the Dirac equation and relativistic tunnelling occurs in an overcritical potential. Relations between this phenomenon and the Klein paradox are discussed. However, the relativistic correction to mesoscopic conduction, the Landauer formula, is negligible and relativistic tunnelling would not occur in solid-state physics owing to the barrier height never reaching the overcritical region. Relativistic tunnelling is essentially a high-energy phenomenon.

https://iopscience.iop.org/article/10.1088/0305-4470/26/4/026/pdf

Barrier penetration and Klein Paradox

Exact solution of the (1+1)-dimensional Dirac equation with vector and scalar linear potentials in the presence of a minimal length

The one-dimensional Klein-Gordon equation is solved for the PT-symmetric generalized Hulthen potential in the scalar coupling scheme. The relativistic bound-state energy spectrum and the corresponding wave functions are obtained by using the Nikiforov-Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type.

Bound-State Solutions of the Klein-Gordon Equation for the Generalized PT-Symmetric Hulthén Potential

We study the problem of the relativistic motion of a 1/2-spin particle in an exactly solvable potential, which consists of the harmonic oscillator potential plus a novel angle-dependent potential, The analytic bound state solutions of the Dirac equation for this potential are obtained by using the Nikiforov–Uvarov method. The wave functions of the radial and angle-dependent parts of the Dirac equation are derived in the form of the Laguerre and Jacobi polynomials. The contribution of the angle-dependent potential to the relativistic energy spectra is discussed under the condition that the scalar potential is equal to or minus the vector potential.

http://iopscience.iop.org/article/10.1088/0031-8949/79/03/035003/pdf

On the exact solutions of the Dirac equation with a novel angle-dependent potential

The exact solutions of the Dirac equation with a linear scalar confining potential in a uniform electric field are given. It is found that, if the scalar potential is stronger than that of the electric field, confinement is permanent. On the contrary, if the electric field is strong enough, confinement is impossible due to the Klein paradox.

https://iopscience.iop.org/article/10.1088/0305-4470/17/4/026/pdf

Su Ru-keng

Papers

Exact solutions of the Dirac equation with a linear scalar confining potential in a uniform electric field