Solution of the Dirac equation with position-dependent mass in the Coulomb field

Abstract

We obtain exact solution of the Dirac equation for a charged particle with positiondependent mass in the Coulomb field. The effective mass of the spinor has a relativistic component which is proportional to the square of the Compton wavelength and varies as 1/r. It is suggested that this model could be used as a tool in the renormalization of ultraviolet divergences in field theory. The discrete energy spectrum and spinor wavefunction are obtained explicitly.

Torsion effects on a relativistic position-dependent mass system

“…At present days, several discussions can be found in the literature with the purpose of showing different ways of dealing with position dependent-mass systems [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Another context has been discussed in Ref.…”

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

“…Although the non-relativistic Schrödinger equation with this potential has been solved for -states [41][42][43] and the single-particle motion in atomic nuclei has been explained quite well, the relativistic effects for a particle in this potential are more important, especially for a strongly coupled system. Solutions have been found and investigated for various cases including the 1D Schrödinger equation with the generalized WS potential using the NU method [44][45][46], the 1D KG equation with real and complex forms of the generalized WS potential [16], the one-dimensional Dirac equation with a WS potential [47], the ( )-wave Dirac equation ( = 0 i.e., κ = −1 for spin and κ = 1 for pseudospin symmetry) for a single particle with spin and pseudospin symmetry moving in a central WS potential [48], the three-dimensional Dirac equation for spherically symmetric potentials, specifically shape-invariant Morse, Rosen-Morse, Eckart, Pöschl-Teller, Scarf, WS and Hulthén potentials [49][50][51][52][53][54][55][56].…”

Quantum Effects on an Atom with a Magnetic Quadrupole Moment in a Region with a Time-Dependent Magnetic Field

“…It is worth pointing out that in the context of condensed matter physics, scalar potentials proportional to the inverse of the radial distance have been studied with 1-dimensional systems [45][46][47][48][49], molecules [50][51][52], pseudo-harmonic interactions [53,54], position-dependent mass systems [55][56][57], the Kratzer potential [58][59][60]. Other contexts are the propagation of gravitational waves [61], quark models [62], atoms with magnetic quadrupole moment [34] and relativistic quantum mechanics [63][64][65][66][67].…”