Confined Dirac Particles in Constant and Tilted Magnetic Field

We study the confinement of charged Dirac particles in 3+1 space-time due to the presence of a constant and tilted magnetic field. We focus on the nature of the solutions of the Dirac equation and on how they depend on the choice of vector potential that gives rise to the magnetic field. In particular, we select a "Landau gauge" such that the momentum is conserved along the direction of the vector potential yielding spinor wavefunctions, which are localized in the plane containing the magnetic field and normal to the vector potential. These wave functions are expressed in terms of the Hermite polynomials. We point out the relevance of these findings to the relativistic quantum Hall effect and compare with the results obtained for a constant magnetic field normal to the plane in 2+1 dimensions.Comment: 10 page

Electron trapping in graphene quantum dots with magnetic flux

It is known that the appearance of Klein tunneling in graphene makes it hard to keep or localize electrons in a graphene-based quantum dot (GQD). However, a magnetic field can be used to temporarily confine an electron that is traveling into a GQD. The electronic states investigated here are resonances with a finite trapping time, also referred to as quasi-bound states. By subjecting the GDQ to a magnetic flux, we study the scattering phenomenon and the Aharonov-Bohm effect on the lifetime of quasi-bound states existing in a GQD. We demonstrate that the trapping time increases with the magnetic flux sustaining the trapped states for a long time even after the flux is turned off. Furthermore, we discover that the probability density within the GQD is also clearly improved. We demonstrate that the trapping time of an electron inside a GQD can be successfully extended by adjusting the magnetic flux parameters.Comment: 10 pages, 7 figure

Relativistic shape invariant potentials

Dirac equation for a charged spinor in electromagnetic field is written for special cases of spherically symmetric potentials. This facilitates the introduction of relativistic extensions of shape invariant potential classes. We obtain the relativistic spectra and spinor wavefunctions for all potentials in one of these classes. The nonrelativistic limit reproduces the usual Rosen-Morse I & II, Eckart, Poschl-Teller, and Scarf potentials.Comment: Corrigendum: The last statement above equation (1) is now corrected and replaced by two new statement

A Novel Algebraic System in Quantum Field Theory

An algebraic system is introduced which is very useful for performing scattering calculations in quantum field theory. It is the set of all real numbers greater than or equal to −m2 with parity designation and a special rule for addition and subtraction, where m is the rest mass of the scattered particle

Finite-Series Approximation of the Bound States for Two Novel Potentials

We obtain an analytic approximation of the bound states solution of the Schrödinger equation on the semi-infinite real line for two potential models with a rich structure as shown by their spectral phase diagrams. These potentials do not belong to the class of exactly solvable problems. The solutions are finite series (with a small number of terms) of square integrable functions written in terms of Romanovski–Jacobi polynomials