Energy Spectrum of a Dirac Particle with Position-Dependent Mass Under
the Influence of the Aharonov-Casher Effect
BRAZILIAN JOURNAL OF PHYSICS, 49 (6):
801-807 (2019)DOI: 10.1007/s13538-019-00707-z
Abstract
In this paper, we investigate the influence of the Aharonov-Casher (AC)
effect on the relativistic and nonrelativistic energy spectra of a
neutral Dirac particle with position-dependent mass (PDM). To exactly
solve our system, we use the projection operators left-handed and
right-handed. Next, we explicitly determine the energy spectra for the
bound states of the particle. As a result, we verify that the
relativistic spectrum depends on the quantum numbers n and m(l), AC
quantum phase phi(AC) generated by AC effect and of the parameter kappa
that characterize the PDM. In addition, this spectrum is a periodic
function and increase in absolute values with the increase of phi(AC).
We also verify that the energies of the particle are minors that of the
antiparticle, and in the limit of the constant mass (kappa -> 0) the
rest energy is recovered. However, in the absence of the AC effect
(phi(AC) -> 0), the spectrum still remains quantized in terms of n and
m(l). Finally, we analyze the nonrelativistic limit of our work, where
we obtain an energy spectrum with some characteristics similar to the
relativistic case. Making an analogy with some works of the literature,
in particular with the hydrogen atom, we note that our nonrelativistic
spectrum provides the so-called binding energies, while that its
absolute values provides the so-called ionization energies.